You can receive any rarity of card from any level of Safe House. To check the rarity drop rates, tap on the "i" button next to 'See Rewards' when you view its information. You can also see how many cards or coins you'll get from this screen.
The number of cards or coins you'll get is based on how many survivors you are dropping off, your Player level, the Safe House level, and any bonuses for being the Safe House Leader or Founder.
If you have no survivors with you when you check the Safe House information, you'll see how many cards you would get for dropping off one survivor.
When a Safe House levels up, you receive a reward of coins based on the number of survivors you left there over the last level.