Compatriot Brad McGee, a manager at Alberto Contador's Saxo Bank-Sungard team, and RadioShack boss Johann Bruyneel are understood to have been fined 200 Swiss francs ($220) apiece after tempers became frayed before the start of the Sunday night (AEST) stage two team time trial.
Commissaires from cycling's world governing body, the UCI, made widespread checks of the riders' specialised time trial bikes before the stage to ensure the saddles were horizontal to the ground.
"Behind the scenes, the bike control was nearly ridiculous today," Evans said on his website diary.
"The French commissaires, (with us) having ridden our same bikes/positions all year, then come here and not be allowed to start unless you change them, a bit of unexpected stress before the start."
He likened it to police officers enforcing the speed limit in different countries, saying Italian police give drivers 20-30km/h leeway and in Australia it is only 2-3km/h.
Evans also noted that with different saddle shapes, the horizontal rule can be nearly impossible to enforce accurately.
A rider will sometimes tilt his saddle slightly forward, especially on the ultra-aerodynamic time trial bike, to generate more power.
According to the cyclingnews website, the UCI had told teams last month that saddles should be parallel to the ground for time trials.
But there was a feeling among team officials and riders that commissaires were suddenly cracking down on the rule.
"Today it was out with the spirit level to check that everyone seats were 'horizontal' as the rules state," Evans said.
"Check any seat with a scoop or channel in the back and that rule has a wide grey area of interpretation, a lot more that can be measured with a spirit level anyway.
"And the hard fast rule for cyclists - 'never change anything on race day' - ha, bad luck if you want to stay in the Tour.
"I noticed a few fines accumulated by sports directors who were arguing their point."
Evans said after his bike check, the BMC team had to move the nose of his saddle up by two millimetres.
He described the change as "just a little more unhealthy and uncomfortable.
"Not to worry, tomorrow we move back to a more normal road stage, 'normal' as far as the first week of the Tour goes anyway."