The low energy plasma blasts are absorbed by the lightsaber on contact
Being a training remote, its blasts are less powerful than normal blasters.
When any blast hits a saber blade, some of the energy is absorbed into the blade and then, if the blast was strong enough, the excess energy is reflected off the blade into a different direction.
Blasts that weren't that powerful to begin with, like the training remote, would simply be absorbed rather than bouncing off in a different direction.
This is supported by the Wookieepedia page on Remotes:
Many Force-users (such as the Jedi Younglings) used remotes as training tools to hone blaster defense abilities by deflecting the remote's low energy plasma blasts with their lightsabers.
The fact that it says low energy plasma blasts supports the explanation provided above. The remote's low energy blasts are absorbed on contact. Normal combat blasters would have high energy blasts that can't be fully absorbed on contact and thus they are reflected off into a different direction.
NOTE: Eumel's answer claims the remote fires bolts of electricity rather than plasma. That, however, is contradicted by the Wookieepedia page on Remotes, which states remotes fire "low energy plasma blasts".