Does tinted moisturiser mean that i don’t need to put on normal face moisturiser first?

It depends on your skin and the brand of tinted moisturiser you use - some are more moisturising than others and if you’ve dry skin then the tinted won't go on evenly without some moisture underneath.

I wear tinted moisturiser and use a serum underneath - that's enough for me.

By the way that answer about using ordinary moisturiser under your eyes is rubbish. Eyes creams are just ways for the cosmetics company to get you to spend a vast amount of money for a tiny pot of something unnecessary.

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Answer:
WRONG, YOU STILL NEED A FACE MOISTURISER, YOU SHOULD USE ONE WITH LIKE SPF 25, ALSO YOU SHOULD USE A CLEANSER BEFORE YOU MOIST. AND NEVER PUT ANY FACE MOIST. OVER YOUR EYES. YOUR EYES NEED A SPECIAL EYE CREAM, IF YOU DO USE REGULAR MOIST. ON OR AROUND YOUR EYES YOU CAN GIVE YOURSELF WRINKLES. I AM A MARY KAY CONSULTANT SO IF YOU NEED ANYTHING AT ALL, PLEASE ASK, I WOULD BE SO HAPPY TO HELP.

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Answer:
If it is moisturizer, then yes you don’t need to use another moisturizer.

But the problem is that brands market their products in a misleading way so it depends from brand to brand.