Preface: I am a benefits administrator at a PEO.
PEOs are the employer of record for all federal taxes and for SUTA taxes in the majority of states. There are only a handful of "client reporting" states, wherein the PEO acts as the reporting agency but files and pays SUTA under the client's name/EIN - Missouri and New York come to mind. SUTA claims in PEO reporting state fall back on the PEO at least while the client is still with the PEO and in some states even after the client leaves the PEO.
PEOs are also permitted to, and most do, sponsor health and welfare plans for their worksite employees. There is nothing, legally speaking, that prevents a client company from sponsoring their own benefit plans but most PEOs require the client companies to adopt the PEO's plans in their service agreement. Of those that will allow a client company to adopt their own plans, most will not touch them for anything other than payroll deductions, which are given back to the client on the payroll invoice.
To answer your original question, it depends on who the plan sponsor is. If an employee works for a worksite employer (client) and is covered by a health plan that is sponsored by the PEO and that employee later moves to another worksite employer that also offers the PEO's health plan, the waiting period should not start over (unless there was a significant lapse of time between DOT at the first worksite employer and DOH at the second). If the health plan was sponsored by the worksite employer, the waiting period would start over unless both worksite employers offer the same plan - IE: Company A and Company B are commonly owned but are separate legal entities so they have separate contracts with the PEO but share the same (client sponsored) health plan and all employees of A and B are covered by that same client sponsored plan.
It is theoretically possible that the PDs of the PEO sponsored health plans could require the employee to satisfy the WP again if they change worksite employers AND those worksite employers aren't related to each other in any way (common control or ownership) but I would be something more than shocked if this were actually written into the PD....that would be an ERISA/125 nightmare and I don't know anyone who would want to deal with that kind of a loophole.