Yes, besseae climbs, this is why each growth is above the last.
Yours is not as bad as my besseae hybrid. See these photos for the way I've been advised to cope with the climbing nature of mine. You can see in the second picture how the new growth is already climbing again.
The grower I bought this from also advised that they do pot so that the newer fans are at the surface, even if that buries an older fan. Sure enough my plant has a part buried fan.
They said they use the upper pot like in my photos to root the higher fan, then next time they repot they used to remove the lower fans and repot the upper one in the medium (the upper one should already have it's own roots at this point). However they discovered that if they left the lower fan on the plant it was possible new growths would come up out of the medium from it.
In fact on mine there is a part buried fan, a fan at medium level, a fan in he upper pot just starting roots. There is then a new growth from both the fan at the level of the medium in the lower pot, and another large new growth coming from the base of the fan in the upper pot.