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 (1e-5) and minimum order size increment is 0.00000001 BTC (1e-8). You can place an order for 0.00001001 BTC, but not 0.00000999 BTC.
You can view every trading pair's respective minimum order size and minimum order size increment here.