This is very much expected. In multiplayer the game needs to be synchronized over the internet. In order to do this, any command you send needs to be shared with all clients before processing it. More precisely, a client need to send the command to the host, then the host shares it with all clients. Hence when you give a command it is only executed a little while later. IIRC this "delay" is hardcoded to be .6s (or .4s?, whatever). In future we might implement having this time "dynamic" i.e. it would be as low as possible depending on the used network connections (this also related to the idea of "variable turnlengths"). This would make the game more responsive in some situations, in particular two computers on the same network.
However do notice that there will always be some delay. In particular, if you are playing with someone on the other side of the globe, you will have at least .133s delay (we need to travel from the client to the host and back, so basically travel a full circumference of the earth). Simply by the laws of special relativity (nothing can move faster than the light). Likely this will be even higher, since your signal probably will travel slower and with some detour.