Caixinha went into the match under intense scrutiny at the end of a week which saw him drop veteran striker Kenny Miller from his first-team squad following a heated training-ground post-mortem into the 2-0 defeat by Celtic at Ibrox the previous Saturday.
When Daniel Candeias scored to make it 3-1 for Rangers, who had trailed inside the opening minute, he led a procession of players towards the technical area to embrace Caixinha.
“Yeah, of course, that was telling,” said John, whose own rapid-fire double had cancelled out Danny Redmond’s opener for Accies to turn the game in Rangers’ favour.
“The celebration after Daniel’s goal wasn’t planned, it was something that just happened. We knew we needed to come into the game at Hamilton and show that we are together and that we are up for it. I think we did show that. We definitely owed the manager a performance and that’s what we did.”
Welsh international John, on a season-long loan from Cardiff City, has experienced previous temporary spells during his career so far with Chesterfield and Barnsley.
The 22-year-old insists he has had no difficulty settling into the dressing-room environment at Rangers.
“It’s been fine,” he added. “We are all together in there. Before training, we are all together – whether that’s in the canteen or in the changing room, having a joke or whatever.
“After training, we might all go for a coffee together or stuff like that. All of the boys are together.
“It does take time to gel and bond, so it will be good to get some more minutes on the pitch for a lot of us. But we are all together.”
John is adamant the situation surrounding Miller, which emerged publicly in the hours before Friday night’s game, was not a distraction for the rest of the Rangers players.
“It wasn’t difficult to focus,” he said. “You focus on every game you play in and that’s what we did. We don’t go into any game looking for anything else other than a win.
“Obviously the boys played well. I managed to get two goals, we got another two after that and it was a really good win.”
In what was only his third appearance for Rangers, John claimed his first senior club career goals. He has never scored in 67 games in English football, while his only previous strike in competition was a penalty for Wales in a European under-19 Championship qualifier against Moldova back in 2013.
“I didn’t really expect to score two goals,” he admitted. “To do it from left-back is even better. For the first one, I don’t really score many goals with my right foot, so that was nice. It’s great to score twice but it was even better to get the win.”