Continuity in terms of flight training from an airlines perspective is doing your ME/CPL/IR at one school. One stop modular or full time modular what ever its market name is holds very little weight in their reasoning - its still modular and they will continue to see it as modular whether its done full time or not, they prefer to see your training done with one provider (CPL/IR/ME) and this is where the continuity statement comes from.
Don't pay over the odds on a one stop modular course to tick this continuity box. If your training modular, research your schools and pick wisely.