To transfer out of rbc into tangerine might be a hassle. You'd have to talk to both banks. But you can easily start one at tangerine leaving your rbc money alone. You'll get a good intro rate at tangerine, and if you're well under your TFSA limits then you can easily dip into it as an e fund. Once you have a few months saved for an emergency, you can start investing
The other option if it won't mess up your limits is to withdraw from rbc and deposit at tangerine. The risk is that if you did the math wrong, you'd have to wait until next year to deposit