IMO, no. These are GROUP fanbases, i.e they exist to support group activities. I don't think they necessarily have to support solo activities, especially if it's the solo activities of a member they don't particularly care about. And it is possible to love a group but not really care for some of the members, as long as you're not actively hating on them. But it does look weird to support one member but not the others - I think it should be all or none
So many fanbases from different fandoms get dragged for not supporting all the members "equally" , I feel like it would be a lot less messy if they didn't bother tweeting about any solos at all