The tubers are a natural part of the plant. It is where it stores water to survive the dry season. They are always there on my U. alpina so I assume this is the same for your U. asplundii. I lost my first cutting of this species, and the second is not thriving for me by any stretch. Pyro has had it in cultivation for longer than I have so his advice would be the better I think. I just haven't had mine long enough to have felt it all out, and my plant is 2 leaves less than a half inch high.
I just talked to a guy that has it growing in peat sand and has it flowering to beat the band. I am hoping to get some plants to experiment with, since this grows like a weed for him, apparently.
On the happy side, my U. quelchii is growing like mad, behaving just as I had expected it would and much like U. alpina which I have mastered very nicely.
My feeling now is that these plants want room to groove. They want to run, just as their terresterial counterparts do, and a more shallow container providing more surface seems to be what mine like. My best results are all out of their pots now, growing into adjacent media which I have kindly provided for them in the form if a net of living LFS. Man, my U. alpina IS just going crazy in the terrarium that lets it grow without encumberences like pot rims. I keep the moss happy with daily spraying. I anticipate U. quelchii is going to behave in the same way since it is putting out those feeler stolons over the pot rim.
These are all remarkable plants, and I really hope to master them and get them sucurely into lots of collections. Utricularia will never be for the common CPer's I think, but to me they will always be the most personable of all the CP's. They are all so distinct!
Rattler you just need to relax about these plants. That was one of the things ATim taught me. There is no need for worry, fancy mixes, volumes of light....none of it really makes all that much difference. I have dried many species out BONE DRY and back they come when conditions improve. You can't drown them. Sand, peat, perlite....whatever suits you they will do fine in. Grow them in water and they are pretty happy too. I just use clean peat. I fluff it up between my fingers. Works for 90% of them just fine.
Remember that division is important to good growth and health. In many species, growth becomes exponential after the patch is divided. I am none too gentle about it either, since my nose tells me something is happening that tells the plant to get growing once it is torn up, so I have been trying to rip the stolons, muahahaha. Call me crazy.
If you have U. aueromaculata, you have a rare Utricularia. For me this one is a slow and sparse grower. Mine is responding to warmth, dim light and regular showers of pure water. Mine likes to run, and I divide it even if it isn't densely filling the pot annually at least. Tim flowered this one. I haven't had a chasmogamous flower yet, just the cleistogamous ones, but there should be seed for a friend from that!
Once a month I visit the local U. macrorhiza population and I gather a couple of jugs of water, very microbe rich. I water the plants with this water at least monthly during the warm months and add it to the water trays. This is the only food my plants have, and nutrition is probably always a good plan with CP.