Your mechanic was wrong — you almost certainly need to bleed the brakes. Here’s why:
When you push the caliper piston back to fit new pads, any air bubbles in the system get disturbed. Air compresses (brake fluid doesn’t), which is exactly what causes that spongy feeling. It’s not dangerous yet but it will get worse and your stopping distance is already longer than it should be.
What to do:
Go back to the mechanic and insist they bleed the brakes. It takes 20–30 minutes and costs very little. They open the bleed nipple on each caliper (starting from the furthest from the master cylinder — usually rear right first) and pump fluid through until no air bubbles come out.
Also check: When they pushed back the caliper piston, did they open the bleed nipple or did they force the fluid back into the reservoir? Forcing old fluid back can push contaminated fluid into the ABS module — expensive damage. Ask them what method they used.
Going forward: Any time brakes are opened — pads, calipers, or brake lines — always bleed afterwards. It’s non-negotiable for safety.