Not at all.
Agent Carter Season 1 is firmly set in April-May of 1946, the One Shot occurs in August 1946 (based on the mention of Peggy having been there a few months and the fact it occurs "1 Year Later" after events of CA-TFA's end scenes).
Also, Souza mentions he'd been in LA for six months, so at least 6 months passes between end of Season 1 and beginning of Season 2. Also, based on the mention of it being "hottest day of the year", Summer of 1947 seems the best placement for AC Season 2. That would mean Souza didn't immediately transfer to LA after Season 1 (stuck around for at least 6 months at the old office, maybe due to his feelings for Carter). The horse race is also labeled the "Summer Classic" so summer, 1947 is when Season 2 occurs, just trying to narrow down the dates/month more.
Guess we can just assume that Howard's offer to head up SHIELD (made at the end of the AC One shot) wasn't accepted immediately by Carter... or she was doing so while still employed at SSR... somehow.