No, it doesn't. A charge controller will supply current if the battery voltage is below the boost voltage setting on the controller.
OP - what is the terminal voltage of each of your batteries?
And yes, they should be charged equally if you're going to run them together in parallel, otherwise the higher one will flow current to the lower one. If the delta is great there could be a LOT of current.
I saw your earlier thread on selecting new charge controller. Are you monitoring the new victron with the app? If so, what is panel voltage coming in? What does it say your battery voltage is compared to what you measure them at their terminals?
You say 'high voltages', but where is that high voltage coming from? Looks like you have a 13.8v boost, should be no problem, but would set them for 14.0 at least. They don't need boost duration as once they reach that voltage they are fully charged.