Have a 323, ........ any thoughts that might help us?
A possibility is that you take too long to raise your Asymm, ... you possibly go 'bareheaded' (no jib) for too long and the boat simply slows down significantly. Any boat that is virtually stopped during a sail 'change' will usually heel over excessively when 'restarting' with the newly raised sail ... until back to speed.
If this is indeed the case, suggest that you rig all the asym lines, etc. before furling/dowsing the jib .... then douse and IMMEDIATELY raise or un-sock the aysm - for only a small loss in boat speed.
If this 'helps', then consider to proceed to the next (possible) step of simultaneously dousing/furling the jib and raising/un-socking the asym. (as fast as possible - see note) ... and with the tack-line TAUGHT, then adjust the sheet, and then allow the tack to be raised to it proper position - luff curling at about mid luff. If you raise with a slack tackline the sail will set 'powered-up'; with tack line taught, the sail will be somewhat depowered.
An asymmetrical that is unstable ('billowing' around) during the raising is an invitation to a 'spinnaker wrap' around the forestay. The 'faster' you get the sail up, trimmed and drawing properly ... the less likelihood of a 'wrap.
Note - to do this you should have a mast crane - an extension arm at the top of the mast which holds the head of the spinnaker out and well away from any furler top swivel .... a rotating swivel/foil can easily 'eat' the head of a spinnaker, thus jamming the furler and sometimes a semi-permanent jam-up. A mast crane helps to prevent this wrapping the spinnaker in the top swivel or furler foil.
A correctly trimmed and properly set tack line will allow the luff to definitely 'move' towards windward. As another poster correctly stated many try to wrongly sail an asymm exactly like a jib ... a well trimmed and tackline adjusted asym will have it luff 'reaching' into the windward side of the boat. How much? .... until the luff just begins to 'curl' and the sail remain 'stable'.