I purchased premier earlier this week then realized it was not on the account I wanted it on. I did not receive anything else from Jagex. I have not used my renewd premier in any way so I should get it but I was wondering if I did not use premier vault the previous month and I get finally have prem transferred the next, will I be able to visit the vault twice to make up for missing out that other month?
No, you won't be able to visit the vault twice in the month.
Once the Premier Membership is transferred, its start date on the new account will be the date it was transferred. It won't be backdated.
You probably already know about this page but the jump off point to transfer membership is:
Transfer purchase
I have just purchased another premier instead of having it transferred because I doubt they will even do anything about it. transfer requests are pointless