Tulum is generally a safe place to travel, but it's always a good idea to take precautions when carrying cash. Keep your cash in a secure place, like a money belt, and don't carry more than you need.
It's generally better to exchange currency at home before you leave for your trip. This way, you can shop around for the best exchange rates and avoid the extra fees charged by currency exchange services in Tulum.
The official currency of Mexico is the Mexican Peso (MXN). However, US Dollars are widely accepted in Tulum, especially in tourist areas.
It may be convenient to have MXN pesos in Tulum, so you can get better deals. However, some tourist places will accept USD too.