OMG - I just hate the fact that this is still such a common way of "reducing expenses" in smaller hospitals. (full disclosure: I have been around for maaaannnny years). Another favorite ploy is to eliminate the PBX operator after 5 pm & route calls to the ED unit clerk <srsly?> Some rurals expect the (only) unit secretary to also serve as the ambulance dispatcher. And, of course, there is no pharmacy, housekeeping or food services at night either. . . but I digress.
If you are the charge nurse, you need to be comfortable with the monitor tech's level of competency. Set up your 'rules' and boundaries ahead of time re: your expectations & when you MUST be informed. For instance, anytime the tech has to make a judgement call (e.g., alarm was triggered due to artifact), she must run a strip and show it to you for validation ASAP, changes in rhythm must be reported immediately, etc). Hopefully, you will be able to work together very confidently.
It also helps to have some protocols set up so that if a tele patient's rhythm is "acting up" and requiring frequent nurse responses to assess, you have the authority to temporarily transfer him to a higher level of care until the situation is stabilized.
Make sure you are VERY familiar with Tx NPA rules for delegation. There are a bunch of delegation resources on the BoN site that can be applied to any situation, including yours. Delegation Resource