Hi Michel.
Sorry to hear you ran into this issue. I recently ran into it as well, upgrading my dev environment to 5.3, where we made similar changes to the main timer server as well (we hadn't previously seen it because it doesn't affect single server environments, until now, and at Harvard we had left the ejb-timer-pool setting untouched.
So, what you found is true, Payara uses a different class for their connection pool than what used in Glassfish 4. So if you are upgrading from a GF4 installation to a P5 installation, you may need to change this (and will once you get to 5.3).
The way I did it was to replace the following from the GF4 version of domain.xml:
<jdbc-connection-pool datasource-classname="org.apache.derby.jdbc.EmbeddedXADataSource" name="__TimerPool" res-type="javax.sql.XADataSource">
<property name="databaseName" value="${com.sun.aas.instanceRoot}/lib/databases/ejbtimer"></property>
<property name="connectionAttributes" value=";create=true"></property>
</jdbc-connection-pool>
with (that I copied from the P5 version of domain.xml:
<jdbc-connection-pool datasource-classname="org.h2.jdbcx.JdbcDataSource" name="__TimerPool" res-type="javax.sql.XADataSource">
<property name="URL" value="jdbc:h2:${com.sun.aas.instanceRoot}/lib/databases/ejbtimer;AUTO_SERVER=TRUE"></property>
</jdbc-connection-pool>
And then clear out the generated folder and redeploy.
Let me / us know if that work for you,
Gustavo