Let's concentrate on the Data Adapter side.
I see that the two adapter initialization phases log in parallel, until the following line:
Finished loading Data Adapter ......
Then, the two JMS connection phases should start, deferred to different threads, through
new ConnectionLoopTSQS(jmsHandler, recoveryPause, logger).start();
but only one of them produces some log.

The ConnectionLoop code is not shown.
Assuming that it is the same as in our demo code,
I notice that there is a static member, called phase in it,
that, unfortunately, both of us missed when we analyzed the code for reentrancy.
The member is remembered across subsequent instantiations of ConnectionLoop,
in order to manage the recovery in some way.
Hence, its behavior may be wrong if multiple parallel instantiations of ConnectionLoop are performed.
This is likely the cause of the problem; note that the same may apply to the generator side.

I'm afraid the ConnectionLoop class has to be revised or reimplemented for your use case.
Please, try; we can't go that far.

Anyway, I suggest you adding %t to your ConversionPattern in the Server log configuration file,
in order to get thread information in the log.