My understanding is that it is as of SM 6.3.8 and not necessarily SMGR 6.3.8 that SM forces the use of SMGR's cert and not the default one.
That said, you can check in the Inventory in SMGR and see what certificates (under 'More Actions') and see if that SM is permitting SIP connections with the default cert. If you upgraded to SM 6.3.8 from previous, there was a y/n question to do things the old way or the new way as part of the upgrade.
To make CM work, I think you have to put the cert in /var/home/ftp/pub and import it through a clunky web interface to make CM use a different cert for TLS.
To make Audiocodes gateways work, I had to generate a CSR and a private key, have the CA in SMGR sign it - through the EJBCA - which isn't exactly intuitive if you haven't done it before... and then take that cert generated for the Audiocodes and the SMGR cert and the private key generated with the CSR and put those 3 things into the gateway to get it up.
I've found some things/apps/devices are more permissive and will work happily with just the SMGR cert, and others won't use the certs you provide unless you did the whole validation chain properly - like how some people click "ignore" and go to the web page when it says the cert the page is presenting isn't from a trusted authority, and other people manage their domain security policies to prevent browsers from accepting certs that can't be validated all the way up to a trusted CA.
It can be a pain!