mining is for resources like durantium, antimatter, etc 
for mining you use mining ring and its various upgrades. 

not to be confused with relics which usually have a name like economic relic or culture relic.
for relics you use xeno archology lab or whatever its called and its various upgrades.

right now there seems to be a bug that minor's can hijack your resources as in they place a starbase there and just take it over that seems to be what your describing
as far as i know this is not supposed to happed and i assume they will fix it shortly