Haven’t tried that, but are you sure you are on stand-alone? This sounds like something that could happen in “thru” mode in Serato for example.
I might have some time to test with a CD-player. If it is some kind of AD/DA latency thing (converting the analogue sound to digital in order to be able to add all the FX/EQ and such), it should not be limited to TTs only.
BTW, be sure to sign up to the Denon DJ forums. They have revamped earlier this year and the boards are actively monitored by the tech guys.