Are the regina chains on vertigo prone to rust?? 

Only if you don't oil it every time you wash it.

Most trials bike come with regina as OE and if not maintained i wouldn't say they rust less or more than any other respectable brand of chain

Regina fine, as long as you look after it. Same for majority of chains. Rust is purely a sign of neglect.

Do this : Buy a cheap deep fat fryer (c/w with basket), & a gallon of chainsaw oil. (Non fling, inexpensive,  stays on chain really well ). Put a few inches in fryer.

Remove chain after every trial, especially in winter. : Remove horseshoe clip & put it straight back on end of the chain in the correct  orientation before you remove the chain. That way, you know the chain can go back on in the same direction as it came off.  Remove crud with Wire brush,  then clean in "parts cleaner" !!! with a stiff brush. If you must use unleaded, then be mindful of Benzene carcinogen hazard & wear correct gloves, etc. 

Fire up your newly acquired chain maintenance unit (fryer) on a lowish setting & place chain in basket. Allow chain to soak / impregnate rollers in hot oil for a few minutes. Turn out on to some old newspaper. Allow to cool, wipe it off,  & refit.

As with all the best workshops, worth having a fire extinguisher in the vicinity & small children out of the way. 

I know its a bit OCD, but it has to be done.