This is a very appealing option for low impact tick control, but do they actually diminish the local tick populations significantly?
Do they control more than just the deer tick?
Based on a few sources I've found, it looks like Tick tubes aren't really intended to keep total tick populations down, but rather to keep the number of Lyme disease carrying ticks down. At Larval stages, deer ticks feed on small mammals, like rabbits, mice etc. At adult stage, they go for larger mammals like deer and sometimes humans. The reservoir species for Lyme disease is mice, so the objective is to kill any larval ticks feeding on mice so that they never reach adult stage where they feed on humans, potentially transferring Lyme disease.
The basic idea of the tick tubes is that they are small cotton balls treated with a low-impact insecticide. These cotton balls are gathered by mice looking for nesting material, leading to a mouse den that is toxic to larval-stage ticks.
However, I don't think deer ticks, as a species, need mice to survive as they are rarely the only small mammal in the area. I would suspect you would still find deer ticks, just a lot less carrying Lyme disease.