The statement on the TPE eTicket that "no break of journey is allowed" is not anything to do with the app - it's the way in which the TOC has asked its TIS supplier (Worldline) to implement certain eTicket formats (there are different formats for walk up, Advance, season, and a few other things). It's not actually in the specification at all, and has simply been hardcoded to appear on the eTicket; whether it appears or not doesn't bear any relation to the journey you make, the restriction code on the ticket, or even what type of walk up ticket it is.
The hardcoding dates back to the time (a few years ago) when eTickets were considered to be a trial or experiment. Some TOCs were concerned that the break of journey would generate increased opportunities for fraud using eTickets compared to using traditional orange magstripe tickets. eTickets are, of course, no longer an experiment or a trial and are available on virtually all routes (except for those that cross London, and some TOC geographic areas) now. The "no break of journey allowed" text should have been removed some time ago and carries no weight (and, in any case, you are not made aware of it until you have bought the ticket).
You can safely disregard it and might also wish to ask TPE to remove it.
There is also absolutely no evidence of increased levels of fraud compared with orange magstripe tickets, either.