You don't need to change the RD, just the cassette and chain, when you upgrade to 105 10s.

There are notable advantages in shifting when you upgrade the drivetrain (RD, FD, cassette, chain, crankset), but it comes with a compatible shifter as well. Better chain/sprocket engagement, better shifting upfront. Shifting will be even better with newer cables. The entire drivetrain is designed as a system to give good performance.

Why do you need to upgrade? Is the gear slowing you down? Or just have a hankering to upgrade?

IMO, it's not worth it to upgrade an entry-level bike. Ride it until it breaks then look for a used mid-level bike to upgrade to.