If wanting to say it was to himself, you need the "self" too. Normally for seg selv, which indicates he is indeed alone. Han har tjue minutter for seg selv.
Or if he spends these 20 minutes doing his own business, as opposed to usually having to take care of the kids. Someone came to give him a helping hand, now he has 20 minutes on his own to fix his hair and get dressed before leaving (in relative calm). The aunt is playing with the kids while they're all waiting for him. Han har tjue minutter til/på seg selv.