First of all, the Tester in MT4 does not work with multiple pairs, it can only backtest one.
Otherwise if you have one EA and you put it to work in different pairs, there should be no problem. All trading blocks that have filter settings are by default set up to work with the current pair. Look at the Market settings, it's empty filed everywhere, which means "The current symbol.
If you use "Set "Current Market" for next blocks", note that when you place the EA for example in EURUSD, the EA works with the ticks of EURUSD and is not aware of the ticks flow in the other symbols.