This scenario depicted by the OP was all-too-regular when I used to commute via Redhill. My GW North Downs line train would arrive and a Southern Victoria train would be sitting at the other side of the island platform (pre-pfm 0) - the doors on my train would open and passengers would stream across to the London train just as the platform staff indicated to close the doors and we'd miss it for want of ten seconds - time and again. The response to complaints was always that every single second counted, which was utter rubbish as, apart from anything else, the train in question was booked to stand outside East Croydon for four minutes and had no other timetable clashes on the way there! The fragmentation of the railway into TOCs driven by individual spurious targets has favoured everyone but passengers in so many cases.
Of course, now that GW trains use p0 the interchange is hugely worse still, as it was deemed too expensive to provide (or useless designers didn't consider it) a 2/3 car stopping board for them (£20?) so they stop along the platform, far away from the stairs and outside the canopy!! When challenged on that, the formal response was that the p0 design team has been disbanded and therefore nothing further can be done (so nothing, however small, can ever be changed at Redhill now?!) - staggering ineptitude from the railway.