During a pad change, when you push the caliper piston back in, brake fluid rises in the reservoir and can overflow - a common surprise for first-time DIYers. It is normal physics, but worth managing so you do not make a mess. Here is why it happens and how to prevent it.
Why the fluid rises
As pads wear, the caliper piston extends and fluid moves out of the reservoir to fill the space. When you compress the piston back in to fit thick new pads - see caliper compression tool - that fluid is forced back UP into the reservoir. If the reservoir was topped off, it overflows.
Why a topped reservoir overflows
This is exactly why you should not blindly top off a low reservoir when the pads are worn - the low level was holding the fluid displaced by the worn pads; see can you overfill brake fluid. Push the pistons back with a full reservoir and it spills. Brake fluid strips paint, so a spill under the hood is bad news.
How to prevent a spill
Before compressing the pistons, remove some fluid from the reservoir with a clean turkey baster or syringe down to about the MIN line. Then compress the pistons - the returning fluid brings the level back up. Open the bleeder while compressing (with a hose to a bottle) as an even cleaner method, which also avoids pushing old fluid backward.
Finish correctly
After fitting the new pads and pumping the pedal to seat them - see new pad won't fit - set the fluid to MAX (not over). Wipe any spill immediately. Use the correct fluid and pair fresh pads with quality pads and hardware.