I kind of question the idea of trying to grow vandas in vases unless you know how the original grower managed it or can ask them about it (it's a bit unusual, they usually like to dry out between waterings and need air movement around the roots). As for the bugs, that doesn't sound like anything I'm familiar with, unless they were indeed mites, spidermites or otherwise. As for treatment, I don't know what to tell you - not having pets (loose ones anyway) or kids, I tend to use the big guns where plants are concerned but mites are tough, typical insecticides are not always effective. If you seem to have cleaned them off for now, I'd wait and see if they come back before treating, and then ask around, imx, you'll get more useful info from actual users of various products than from the manufacturer labels - lots of insecticides claim to "control" mites but do a poor job of it and sometimes damage plants, actual miticides are a mixed bag, hard to find in small home-user packaging. Needless to say, if you're not comfortable using "strong" chemicals in your home, you'll have to stick with things like soapy water which are marginally effective but perfectly safe; if you go for proper insecticides, one of things I do to minimize risk to myself is spray plants in the bathtub with the shower curtain pulled semi-around everything, keep windows open and wash down the tub shortly after spraying. Fwiw, I'm still here and still have the appropriate number of heads, limbs, etc (lol)

I can't grow vandas any other way here in the U.K. as the greenhouses are far too cold in the winter and in the house the vases are the only way. Over here they have been sold for some time in the big nurseries and have been imported by them from Holland. I did e-mail the actual growers for some advice before raising questions on this forum,that was two weeks ago and have heard nothing. It seems once they have exported that's the end of it.
Sue has answered my question on the other thread and although I had never seen such small bugs before found the images she suggested on Google and think they must be black aphids. They must have been in the plant roots when I bought it.
I don't know how successful I will be in growing the vandas this way but apart from the deposit in the vases and the aphids (both which have been cleaned up now) the plants seem to be thriving and the blue one has produced a second spike.
I don't have qualms about using insecticides and do use them on other plants but I was too scared to use them on orchids. I think cleaning them from time to time with running water may suffice.
I do appreciate your reply as I expect you are experienced. We novices need all the help we can get and I do hope our questions aren't tiresome.
Thanks again Hazel.