The jettison of spent boosters depends on a number of factors like the design, safety etc.
The Japanese H-IIA has a rather unique design, where the thrust developed by the solid fuel rocket motor (SRB-A) passes through the thrust struts and is
received by the lug which forms an integral part of the cross beam fixed on the LE-7A engine.
Image from Successful Return to Flight of the H-IIA Launch Vehicle by Takashi Maemura et al.
The jettison procedure is initiated when the combustion pressure reaches 2%. The forward and aft yaw braces (which transfer the radial component of thrust) are cut off by the ordnance system, and the booster assembly (that is held by thrust struts) departs from the launch vehicle, and is completely separated after about two seconds at the point where the thrust struts are cut off.
Image from New H-IIA Launch Vehicle Technology and Results of Maiden Flight by Takashi Maemura et al.
The main concern during jettison is safety, so that (either of) the boosters don't have any residual thrust while the jettison process is under way. otherwise, the transfer of thrust through the thrust strut will make the vehicle unstable.
Another end of delayed separation is the Delta II rockets, which carry their spent casings till they reached their preset drop zones (well after burnout) to clear offshore oil platforms.