Yep, I have the same experience in Reaper. Multiple instances will progressively introduce more delay on playback starting, no matter if they have zero samples or phrases loaded. I can actually enable ‘Flush FX on stop’ in Reaper settings to introduce the same exact lag/delay on playback stop.
It’s not a dealbreaker for me as I mainly use Redux for programming drums or breaks + bouncing sequences to audio, so rarely have more than one or two instances per project, but I can see it being absolutely intolerable for anyone who wants to use lots of Renoise instruments in one project.
It’s plausible to me that the lag/delay is some necessary part of having phrases work properly or sync up with the host, but it happens even without using phrases.