When Federer was looking for a training partner ahead of his return to clay in Madrid earlier this month, it was the British number three who got the call and happily accepted.
"He was so down to earth off the court," said Evans. "It was a bit surreal sometimes how we ate lunch and stuff - he didn't hide away or anything.
"He didn't change his day because people were going to come up to him. We went to a golf club for lunch, we went to a pretty average tennis club for lunch as well, so it was just normal.
"How he goes about his business and his practices, I was pretty surprised with how simple a lot of the drills were and it was a bit of an eye-opener to what's being done in our country (compared) to what the greatest tennis player of all time does."
LTA performance director Simon Timson is a big believer in sports science but Evans thinks the governing body's focus should be on increasing the number of players making professional strides.
"Let's maybe get the basics right, walk before we can run would be good for me," said the 28-year-old, who did offer strong support for the LTA's return to an academy system for the leading juniors.
"We need more people (ranked) inside 200-300 before we start having analysis and stuff like that.
"The people who are running performance obviously don't think it's wasted (money), they want to put their money into that. People are using it so it's not wasted but I think it could be spread out a little better.
"In our country you can't be a tennis player when you have no money or you're from a bad area. It's impossible unless your mum and dad remortgage their house. Why should people do that when there's six analysis guys?"
Press Association Sport has contacted the LTA for comment.
Evans' practice partners ahead of his return to Roland Garros for the first time since his year-long drugs ban have also included Andy Murray at Wimbledon.
The former world number one has begun to increase his workload as he builds up to what he hopes will be a return to the sport, perhaps on grass in doubles.
"He was great," said Evans. "He seemed pretty happy - if I'm honest, a bit happier than normal. Hopefully he can come back and get going again."
Evans avoided clay for much of his career but has produced some positive results on the red stuff this season, most notably a victory over 31st-ranked Dusan Lajovic to qualify for the Italian Open in Rome last week.
He will be hard-pressed to claim a first victory at Roland Garros, though, having drawn 23rd seed Fernando Verdasco.
"Difficult," said Evans when asked about his draw. "He's obviously a good player, he's had a pretty decent clay-court season.
"Everyone knows he's got a big forehand so I'm looking forward to playing against such a good player and test myself.
"I feel I've played pretty well, I feel way more comfortable on it. I had a good few days in Rome and obviously had a good chance in the first round. I'm still learning a bit."