Yes, it's perfectly normal.
Shooting down UFOs triggers Retaliation, which searches for your base and attacks it.
On Superhuman, the chance to trigger is 20% per UFO shot down... so in average shooting 2-3 UFOs already triggers it.
They usually find you in about a half a month or less...
If you play on high difficulty... don't shoot down UFOs early.
PS: beginner 4%, experienced 8%, veteran 12%, genius 16%, superhuman 20%