Yes, regular browsing rates will apply when going outside YouTube, unless you’re registered to a surf promo.
To keep your load safe from unexpected charges, try registering to SurfAlert! Surfalert sends you free notifications every time you go to a chargeable site and you’re not on a surf promo. Learn more about it by dialing *143#, then select MyAccount > Mobile internet usage > Turn on mobile internet alerts > SurfAlert.