We talk about several topics on this thread, but all about tap and tempo and timing, so let me bring some structure into this discussion.
The Profiler has an advanced tempo and timing engine, inherited from the Access Virus Synthesizers. Keyboarders have very strong demands in the timing machine, especially to run arpeggiators synced along a DAW.
The tempo engine receives information from the tap button (hardware or midi CC) or an incoming midi clock, or the BeatScanner.
Effects like delays or the tremolo run on the tempo engine.
Delays are easy, because they only need the right tempo, the timing is made by you playing your instrument.
You might be used to tap four times to set the tempo on other devices. However, it's a good idea to tap more often. The Profiler adapts to your tempo with every tap, for an infinite time. It will even follow tempo changes quite smoothly while you tap.
When synced to an external midi clock, you might observe tempo deviations. What you see is the timing engine constantly adapting to the incoming tempo. The visible tempo variations have no impact to the audible result. If you have experienced that other devices don't show tempo variations, than those manufacturers hide it by showing a highly averaged tempo. The result should be the same however. If you see the tempo deviate by small one digit numbers, then everything is ok. If you see two digit deviations caused by incoming midi clocks, then your midi interface is of bad quality and causes timing jitter of dozens of milliseconds. It is worth to be mentioned that today and since 20 years, the majority of midi interfaces have a terrible timing, unfortunately.
The tremolo effect is a different beast. Here it's about the tempo AND the alignment to the beat, similar to an arpeggiator.
The tempo engine has a special feature for realigning the tremolo: Whenever you press TAP after a certain time on a downbeat, the tremolo will shift to the timing of that tap smoothly. But don't tap too often, as it would sense it as a new tempo. Perfect is to place a single tap sometimes at the beginning of a new bar, even every bar is fine.
Now this goes to hackowl . In many years we had no user syncing the timing of the tremolo to an external midi clock and reporting problems. But it does not work right the way you use it. I just took the time to look into the tremolo code and was happy to have fixed a quirk a few minutes ago. While the tremolo always played the correct tempo, it was easily going of beat, as you have showed up. Please check the next upcoming software update and tell me your experience!