I don't know why Bulbapedia ignores official sources when they have it on their own fucking page.
Source is Toshinobu Matsumiya:
http://archive.is/D9iPzKanto - Hoenn
--- 3 years gap ---
Johto - Sinnoh
--- 1~2 year gap ---
Unova
--- 2 years gap ---
Unova 2 - Kalos
--- 2 years gap ---
Alola
So if Wally started his travels at 10, he's 18~19, add one more if you think he started aged 11, and so on. Still legal, but nowhere near 30.
In other words, he is Pokemon's Honey-senpai, if you know who that fucker is.