The Hammers had already convincingly beaten Arsenal and Liverpool, both away from home, before Monday night's comfortable 2-0 win over Newcastle United at Upton Park.
Slaven Bilic is playing a more attacking style based on keeping possession, far removed from the tactics of previous manager Sam Allardyce.
Bilic has players and fans united in excitement
And it is not just the affections of fans the attacking style has won but players too, with Jenkinson telling the club's official website he has high hopes for the season.
"It is exciting to play in a team like that," Jenkinson told whufc.com.
"We have got a lot of power and ability going forward and it is about utilising that. I think that style of play (counter attacking) probably suits us when you look at the type of player we have brought in and the way we want to play."
Competition is fierce for on-loan Gunner
Ironically, after being one of West Ham's best players last season, Jenkinson may find it harder to keep a place in the first team nailed down this time around.
Of West Ham's three wins from five games so far this season, James Tomkins has started at right-back in the Arsenal loan ranger's place. Jenkinson endured a tough afternoon when he was at fault for two goals and got himself sent off in the 4-3 home defeat to Bournemouth.
With Tomkins starring in his place during a historic 3-0 win up at Anfield, he rightfully kept his place in the side to face Newcastle.
Injury provided chance
Jenkinson did get a chance to redeem himself, though, when he replaced the injured Angelo Ogbonna in the first half.
Tomkins moved inside while Jenkinson took up the right-back position and, although he started somewhat nervously, the England Under-21 man grew into the game as the Hammers won 2-0.
As an Arsenal player, Jenkinson should fit in perfectly with Bilic's style of play given he is used to keeping the ball on the ground and attacking at pace under Arsene Wenger. If he can return to the standards he set during his first loan spell, meanwhile, Jenkinson will be crucial to the Hammers enjoying their last ever season at the Boleyn Ground.