It may be the result of a lack of communication compounded with enforced secrecy.
In Black Widow’s mid-credits scene, Yelena, the breakout character played by Florence Pugh, was put on the trail of Jeremy Renner’s Clint Barton/Hawkeye, teeing up multi-episode arc on the Renner-fronted Disney+ show that began this week.
When Marvel added that scene, the Hawkeye team was already writing Yelena into their show after head writer Jonathan Igla lobbied to include her in the series. One day, Igla got word from Marvel Studios boss Kevin Feige that Black Widow would include a post-credit scene leading into Hawkeye, but he had to keep that to himself to preserve the secret as long as possible.
TL;DR, they'd already written much of the script for Hawkeye when Igla found out that Yelena would have a mid-credits scene with Valentina in Black Widow, they didn't have details on what that would involve, and Igla felt they couldn't even relay that the scene would happen without risking revealing spoilers, so there wound up being a disjoint.
There are, of course, fan theories, including the idea that Yelena is either fibbing a bit about who hired her, or this is all part of Valentina's machinations to get Kate, as "the next Hawkeye" onto her team as she has John Walker ("the next Captain America" at one point) and Yelena ("the next Black Widow").