Secondary car battery voltage
When you connect two batteries in parallel such as when your relay turns on, the two batteries will "fight" each other to equalize the voltage. Essentially, the higher voltage battery is trying to charge the lower voltage battery. If the lower voltage battery cannot take any additional charge, the combined voltage will be roughly the average voltage of the two batteries.

The word "roughly" is used because it actually depends on the internal resistance of each battery, the resistance of the wiring between the batteries, the voltage and amperage capacity of the alternator, and the state of charge of both batteries.

In general, I would say your circuit is working as expected given the possible variations of the installation.