In the VST select the manual start option. Then in the options menu go to the background sync and transport quantize option and for manual transport quantize interval select next bar. Then you should be able to go into the midi panel settings and "learn" a midi value for selecting the manual sync button. This can be from a controller value on an external controller. Either that or you can put the midi controller value into a midi track assigned to have the Sync Gen VST as its target and just make sure that the midi controller appears after the first measure but before the second one.
When recording I've set Logic to do a 1 bar pre-roll, but playback pre-roll is only about 1 beat. At the start of recording, the Sync Lock starts up 1 bar earlier than everything else. But when in playback, the Sync Lock appears to start up at the same time as everything else at 22.214.171.124
Does Samplitude have recording or playback pre-roll that can be adjusted? Logic's playback pre-roll seems fixed.