>
> My bet is that there are various APIs which could be used and this is 
> behaviour of some API emacs uses (at least in this build and in this 
> environment). I didn't see this popup „before problem started” (on older 
> Ubuntu) – then IIRC emacs composition worked silently, character 
> appeared only once fully entered.
>

Can you perhaps try to play with the various values of the inputStyle X 
resource, by starting Emacs like this:

emacs --xrm 'Emacs.inputStyle: callback'
emacs --xrm 'Emacs.inputStyle: offthespot'
emacs --xrm 'Emacs.inputStyle: overthespot'
emacs --xrm 'Emacs.inputStyle: none'
emacs --xrm 'Emacs.inputStyle: root'
emacs --xrm 'Emacs.inputStyle: native'

Does one of these invocations solve your problem?