McGuigan and father Barry, the former world champion, signed Taylor to their Cyclone Promotions company when he won 2014 Commonwealth gold and turned pro.
"I thought you saw the complete article," said Shane McGuigan of the man from Prestonpans in East Lothian.
"He looked like he could punch - now he can really punch since changing the technique a bit."
In addition, the trainer said he was keen to work with Taylor because "he has a great personality, he's a good-looking lad, he's fast and he can really fight - he ticked a lot of boxes".
He added: "Also, I felt dad, with his background, a hall of famer, being a Celt himself, can appeal to a lot of the public in Scotland."
Taylor left Edinburgh's Lochend club, where he worked under Terry McCormack, and now trains for his pro fights at the McGuigans' gym in Wandsworth, south London.
He is aiming for a 10th consecutive win when he defends his Commonwealth super-lightweight title against Hackney's WBC Silver champion Ohara Davies at Glasgow's Braehead Arena on 8 July.
"Josh is a phenomenal talent, a phenomenal force," added McGuigan junior.
"He's been pro for a short time and he's already the Commonwealth champion and within six to 10 months he will be knocking on the door of a world title.
"We've been working together for nearly two years now and he has excelled so quickly.
"He has come out of the elite level amateur system and he is still progressing.
"He has shown me so much in the gym and now it is our chance to really showcase that talent on the main stage in front of big audiences on television and at Braehead."
Cyclone Promotions hopes Taylor will generate the same level of appeal as his stablemate, Belfast's Carl Frampton, a two-weight world champion.
"With Carl, we built him up at home and then we took him to America and then to Manchester for a unification fight," said Shane McGuigan.
"That's the same sort of platform we would like to set up for Josh Taylor.
"We'd like to make him a star back home in Scotland and then filter him out to London, Manchester and the bigger arenas and then eventually go to the States. That is where he is inevitably going to end up, that's where the money is.
"It is very rare that you have the Errol Spencers coming to fight for world titles over here. If you build loyalty with your fans they will go anywhere."
The McGuigans have already had Taylor on the road, with three of his nine fights being in El Paso, New York and Las Vegas.
"The American public loved his crowd-pleasing style, just like they loved Ricky Hatton," said the trainer.
"People want to see a good fighter go to work and they will get that with Josh Taylor."
Shane McGuigan is anticipating a "tricky" fight against undefeated Davies next month, expecting it to go to the later rounds.
However, he believes the home fighter will prevail and take over the mantle of Ricky Burns, for so long Scotland's main boxing attraction but who, in April, lost his WBA belt in Taylor's weight class to Namibia's IBF champion Julius Indongo.
"Ricky Burns has been a fantastic ambassador for Scottish boxing and a great champion but I don't see him reclaiming any world title; he's a step below that now.
"Josh Taylor is the man. He is going to be holding the flag and going on to bigger and better things. If he can inherit some of Ricky's fans then that would be fantastic."
Scotland's Josh Taylor has all the elements it takes to make it to the top in boxing, says trainer Shane McGuigan.