They have both enjoyed dream runs against seeded players in Shanghai, including Rinderknech beating world number three Alexander Zverev on Monday.
The 54th-ranked Frenchman followed up by defeating the 15th-seeded Czech Jiri Lehecka 6-3, 7-6 (7/5) on Wednesday to advance to his first quarter-final at the Masters 1000 level.
Vacherot, from Monaco, is 204th in the world and became the lowest-ranked player to reach the last eight in Shanghai on Tuesday.
"Our family WhatsApp groups are for sure buzzing a lot the last few days," laughed Rinderknech.
"It's really reuniting the family together... everybody is watching each other. So it's really cool."
Rinderknech and Vacherot both attended Texas A&M University.
"I said you need to follow me... I recruited him," said Rinderknech.
After overpowering Lehecka in a second-set tiebreak, he wrote on a camera lens: "I follow you, Val."
Adding to the family pride, Vacherot is coached by his half-brother, Benjamin Balleret.
His last season was beset by injury, and he had to come through qualifiers to reach the main draw in Shanghai.
"So much emotion just thinking of the tough times I had," said Vacherot, on the verge of tears after beating 27th seed Tallon Griekspoor of the Netherlands on Tuesday.
"Just to share that with my coach, brother, my girlfriend - it's unbelievable and I'm having one of the best times in my life right now."
Rinderknech said he had "always known what Val is capable of".
"The toughest thing... (is) to be able to align all the planets... And that's what he's doing," he said.
"I'm not surprised. I'm really glad and happy for him, for Benjamin as well... it's such a credit to both of them."