Twin A finds twin B as younger than himself, hence he says that B experience time dilation.
No. While in relative motion they both consider/know that time is slow for the other. That's what is called "Time dilation".
And it goes both ways - it's reciprocal. After all, that is what puts "paradox" in "twins' paradox". (But to be clear, it's not actually a paradox, there's is no argument about that. The term comes from a naive partial understanding.)
On the other hand, Twin B finds twin A as older than himself, hence he says that A experience time contraction.
That one turns out a different age than the other is usually called "differential aging".
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