How to use the stop limit order/ stop order in Tiger Brokers?

Let's say I wanted to buy a stock at $100 and wanted to cut loss when the price go down by 5%, which is $95 by this case. From what I experienced from the Tiger Brokers desktop stop limit order feature, I set the limit price at $100 and stop price at $95, which means the system will place my buy order when the price reach $100 and if the price go down to $95, the system will place the sell order. But instead the system placed the buy order when the price reach $95. Is this the limitation of the broker or my mistake when placing the order?

You misunderstand what a stop limit order does. You should read the various order types info on Tiger website here:

https://www.tigerbrokers.com.sg/help/detail/ord...

The system is doing exactly what a stop limit order is supposed to do in your case.

In order to do what you want, you do the following:

You place a buy limit order at $100.
When the price reach $100, the system will buy the stock at $100 or lower.
Then you place a sell stop order at $95.
When the price drop to $95 or lower, the system will trigger a sell market order, which will sell your stock at whatever market price at that moment.

If you want to automate step 3, you can use the Additional Order type described in the above link. The Additional Order will consist of a master order (buy limit order at $100) and a sub-order (sell stop order at $95).