Do I still need tweaking after using gm/Id method if some of the MOSFETs are not in saturation?
Does gm/Id method guarantee the transistors are in the saturation?

No, the biasing of the MOSFET determines if it is in saturation or not. Note that also a large signal can push a MOSFET (temporarily) out of saturation.
Realize that the \$gm\$ of a MOSFET is a small signal parameter and the value of that \$gm\$ depends on the mode of operation (linear / saturation), size of the MOSFET and biasing current. So the value of \$gm\$ will change when the MOSFET changes its mode of operation.

What should I adjust after using gm/Id method if some of the MOSFETs
are not in the saturation?

For designing amplifiers etc, you generally want your MOSFETs to operate in saturation mode. If a MOSFET is operating in linear mode then ask yourself if that is really needed. So in general if a MOSFET goes out of saturation then you need to change the biasing such that it will stay in saturation mode. By &quot;change the biasing&quot; I mean any action that changes the operating point of the MOSFET. If the drain current has to remain the same then changing W/L still changes the operating point.