Yes, age matters at the border. Duty-free allowances for alcohol and tobacco apply only to travelers above the relevant legal age, which most countries set at eighteen for these purposes, with some, notably including several that use twenty-one for alcohol, setting it higher. A minor cannot import these goods duty-free, and adults cannot legitimately spread their excess across their children's nonexistent allowances, a trick customs officers have seen a thousand times.
Enforcement is uneven but real. Officers rarely card obvious adults, but anyone youthful-looking carrying alcohol or cartons of cigarettes can be asked for a passport check, which of course states the birth date anyway. Duty-free shops at departure and arrival also apply age checks at purchase.
Note the import age and the local purchase or consumption age can differ, and the stricter rule effectively governs. If you are traveling with someone underage, keep the restricted goods clearly within the qualifying adult's own allowance and luggage. The destination's customs site states the age thresholds alongside the quantity limits.