in neutral movement can be kinda tough since everything obvious will lead to you getting antiaired, i cant just give you a definitive way to play it since everyones gonna be different in that aspect but i'll just jot down whatever i can think of:
after using a followup to get to the opponent you should almost never go straight in, you usually want to cancel into another chain before reaching them, this way they if they tried to antiair the first chain they get hit by it giving you a combo. If they don't antiair however you usually go with one of two options, depending on how close you are (and how fast the opponents antiair is), you can press D followup followed by a j.B, if you're close enough they usually cant do an actual antiair as the startup is too long, so they're forced to either use another button (usually 5a), or block, generally i think this option is a bad idea since believe it or not 5a antiair works a LOT more often than you'd expect, but as with everything its good to mix it in occasionally to keep the opponent guessing.
the second option is cancelling into j.214B or A followup, and either 1. Continuing on foot, or 2. backing off to regain your stock(s). if you're close enough you think you can gain pressure with a 662b than you should go for it, j.214b lets you immediately cancel into a dash if it whiffs so you can cancel into it then immediately 662b once you land (alot of opponents will try and either jump or backdash here, 623D can catch their jump, or a superjump forward can get you back in their face. 5d will either catch their backdash, or force them to block it which puts them back in the RPS), after the microdash you're almost always close enough for a 5b which lets you go into stagger pressure. But if you're not confident you can do it you can back off, and play a little defensive for a bit until your chains regenerate.
I mentioned A followup at the start as some people will predict your j.214b, and try to run up and either counterhit you or catch you after landing, forcing you to block, if you hit A followup you have the choice to either try and airdash and get away from/behind them, or attempt to hit them with a falling Aerial button (i prefer hitting either j.A or mashing j.C depending on how confident im feeling).
Now, i said there were were only 2 options which is obviously never true in a fighting game, those are just the main two you should consider. However another option i use alot (i use it way too much, seriously dont do this as much as i do), is if i have a second stock i'll use B followup to avoid their antiair, then try and hit them with a third chain. This does work, but its a relatively rare occurence and when it doesn't you're left like -45 since you dont have any more stocks, and the only option you really have is to hit j.214B and cross your fingers you counterhit them trying to punish, but this is arguably an even worse idea since if they predict it they'll have the most free counterhit of their life.
C followup can also be used after the opponent blocks your chain, the benefit of this is that if the opponent predicts a D followup and tries to antiair you, and the antiair doesnt cover like 20 feet behind them behind them for no good reason (looking at you susan), you'll end up behind them while they're in the animation, letting you hit an aerial button (j.A or j.B usually), and counterhit them (you wont get much damage off of this, but it will let you set your oki up), However this option is countered by delaying your antiair a bit if it gets invuln early (or, once again, just mashing 5A to antiair)
and some random movement tricks:
if you hit j.4d, then press D followup as soon as possible you fly across the screen in an almost perfectly straight line, this momentum can be slowed down by hitting an aerial button (usually j.B, but every one of hazamas air normals has a place to be used here), or completely cancelled with j.214b, if you hit j.6d instead you'll go in a slight upward curve compared to j.4d, falling down once you're around 45% of the way through the screen,
B followup can be used off pretty much any chain to slingshot you around the stage super fast, but it can be a bit hard to control, and because of how fast it is you usually cant cancel into a button to make yourself safe, the more vertical the chain is going the further you're going to slingshot (note that using this trick with 2d in the corner doesnt work, and will instead just kinda swing you up and back down), if im going to use this i prefer doing it off a high j.8d, as it just barely gives you enough time to cancel into j.B or another chain.
one last section, i'll try to keep it quick, this is already way longer than i thought it would be
buttons after chain followups:
j.A is used to trigger your momentum to start decaying a bit faster without too much risk since its fast,
j.B is used to throw out a long hitbox to catch the opponent trying to mash something without head invuln,
j.2c is be used to hit the opponent under you (though its risky), or to hit the ground early since it extends hazamas hurtbox downwards
j.C(CCCC) is generally used to just throw out a hitbox thats going to stay there for awhile (almost always while traveling upwards), you dont see this used often but if you're not confident you're going to time your button correctly you can use it,
j.214b is used to immediately cancel all of your momentum and get to the ground as fast as possible
kinda realized a little over halfway through this i more explained the entirety of neutral when you just said "movement", but i already wrote it all and i think its still good to read anyway, so im gonna leave it.
im *far* from the best hazama and im sure ive said a few things here some 85k match JP player thats played daily since continuum shift is gonna find and call me a complete idiot for, but i dont care, everyone has their own way of going about all this, this is mine.
Anyway,
TLDR:
After hitting a followup to move towards the opponent an early j.B can be used to try and lock them down, or another chain can be used to catch their antiair. if they don't antiair you can either go to the ground with j.214b to try and start pressure or call out their jump/backdash, or hit A followup to try and avoid a punish. Other less reliable options include using a second stock to press B followup, followed by a third chain, or pressing C followup to try and avoid their antiair by going behind them. Pressing D followup immediately after a j.4d or j.6d will launch you in a straight line forward, and Pressing B followup after a chain shooting up will slingshot you forward. After a chain followup j.A slows your momentum, j.B throws out a big hitbox to lock down the opponent, j.2C lets you hit the ground early or hit the opponent below you (risky), mashing j.C can be used to cover up poor timing by throwing out a long (duration-wise) hitbox, and j.214b can be used to immediately stop all your momentum and get to the ground.