I'm only 12 and I have my vibrato. I have only been singing for 5 years! Is this normal?
It's relatively rare, to be sure - you are listening carefully enough to have noticed, which is a great thing! So keep listening - notice how opera singers sing all the time with vibrato, but classical boy sopranos your age usually sing without it, while some classical adult singers (only those performing ancient and baroque music), sing without vibrato but use it as expressive decoration, and other kinds of singers (pop, rock, flamenco, folk, etc.) will change back and forth as well.
My suggestion is to try to think of your vibrato coming in as "this is something else I can do with my voice - but singing in tune is way more important - I can hear intonation more clearly when I sing without it, but the sound is warmer when I use it!". Otherwise you will become so use to using it that you won't be able to sing without it, which would be a shame - keep listening for all the great singing that uses vibrato expressively.