Thanks to all that have responded.
As of now the problem is gone without me changing anything. We'll see if it comes back. The bad thing is that one does not know unless someone tells you or you monitor your transmissions on a separate receiver.
I realized that delayed TX start does not affect the timing (DT). I made a simple test connecting audio between two computers. Started TX on one of them and the decoding on the other was ok with DT 0.2. Broke up the transmit audio path and reconnected it in the middle of the TX sequence. Decoded ok and DT didn't change.
So the problem must be caused by a latency of the transmit audio in the PC or the ICOM audio codec.