Whether an plea of not guilty by reason of insanity plea is a conviction for immigration purposes is still unsettled. In an insanity case, the actual plea is not "guilty except for ..." It is "not guilty by reason of insanity." That is because insanity negates an essential element of the offense: the intent. Therefore, a "not guilty by reason of insanity" finding is arguably not a conviction. Unfortunately, in California and other states, you first have to enter an actual guilty plea prior to being found not guilty by reason of insanity.
One could argue that the ultimate finding of not guilty was equivalent to post-conviction relief based on a substantive flaw in the proceedings. Namely, the lack of intent, and therefore, lack of guilt. Another available argument would be based upon Retuta v. Holder, 591 F.3d 1181 (9th Cir. Jan. 7, 2010), on the theory that no criminal sentence/fine can be imposed following a guilty plea, in some states like Oregon, and the (civil) commitment that can follow is not a punishment/penalty/restraint under INA 101(a)(48)(A)(ii). In Corpuz v. Holder, 697 F.3d 807 (9th Cir. Aug. 31, 2012), the court, in dictum found otherwise, without explanation, but then whittled off enough time through constructive good time credits to enable a respondent to qualify for 212(c) relief with 4 years and 10 months imprisonment, crediting most of the time in civil lock up.

Thanks to Jon Garde, Lisa Brodyaga, and Joseph Justin Rollin