I hope this helped you out a bit at understanding relativity.
I'm pretty sure you got it the wrong way round.

Remember the twin hypothesis; the twin that moves faster ages slower. So he percieves the world around him moving faster.

Imagine your example running for much longer, so that the twin in the accelerator thinks that 40 years has passed, but the twin outside only ages by 20 years. Well... that's the reverse of what the twin hypothesis says.