I believe the answer to that is no, it does not stop you from doing that. I have had this discussion about the Yncarne and it's inevitable death rule, if I deep strike it using that rule during my opponents turn can I then charge during my turn. The answer we came up with was yes, due to the fact that it is stated that unless otherwise specified 'turn' refers to player turn not game turn.
By the same wording, if you did something that prevented you from charging that turn (being your own turn) that would not prevent you from charging on a different turn (your opponents turn).
This was the interpretation that the people I hobby/game with came too, and I have seen a few online views that agree with us, but as far as I am aware there is no certain ruling on that.
To add a little bit more clarification this is the way I am looking at soulburst actions and what is allowed / disallowed:
For my soulburst action I think, if this was my first (shooting/movement/assult) phase what would I be allowed to do. Eg. A shooting soulburst action. If this was my first shooting phase and I have moved in the movement phase such that I can not shoot heavy weapons I would still not be able to shoot heavy weapons, but what I did in my actual first shooting phase (run/turbo boost/etc) doesn't affect what I am allowed to do.
TLDR: Consider what my previous different phases allow me to do, but don't consider previous actions of the same phase in which I am soulbursting. All these things refer to restrictions for 1 turn (player turn) though, so none of these restrictions are in place on the opponents turn.
Through my limited play testing, I have no yet encountered a scenario where this thinking does not work and to me it seems a reasonably fair interpretation of the rules. Feel free to point out if you can think of anything though.