The jobs report is traditionally the most important piece of economic data on any given month. It's even had the power to move the bond market as recently as early 2022 despite the labor market being cemented as a star performer. Now this morning, the jobs report came out roughly in line with expectations, but bonds nonetheless sold off--seemingly in response. But the fact of the matter is that traders often show up to NFP day with trading strategies that aren't based on the NFP results themselves. Today they showed up to sell bonds--at least at first.
Shortly after the initial sell-off, bonds rebounded and linked up with stocks in a more conventional way. In other words, stock prices and bond yields have been moving together since then. This is often a byproduct of traders tapping out for the weekend and setting execution strategies on cruise control. Declining volume only bolsters the case.
Cruise control, in this case, simply means that markets reached their intended destination for the week by yesterday afternoon and the next meaningful input will arrive next week--most likely with an update on inflation via CPI.