Gemini does have trading minimums for our supported cryptos. Trading minimums reflect the smallest amount of a crypto that can be traded on Gemini, while tick size is the smallest quantity increment. Trading minimums and tick size differ by asset. 

For example, BTC has a trading minimum of 0.00001 BTC and the tick size is 0.00000001 which is the smallest quantity increment. You can place an order for 0.00001001 BTC, but not 0.00000999 BTC.

You can view every trading pair's respective tick size and quote currency price increments here.