It'd be interesting to see what the court precedents are. Here, the wildlife law SAYS that scientific names take precedence, but the courts have consistently ruled that BOTH names must apply. If the California courts ruled similarly, then the most likely result would be that ONLY those Ambystoma which are normally called "tiger" would be prohibited, and at worst they might expand it to include the entire subgenus [ie, all the Mexican and western species apart from A.gracile and the A.macrodactylum complex].
For example, the law here prohibits the sale of the following:
Thamnophis sirtalis red-sided garter snake
Thamnophis elegans wandering garter snake
For both of these, the common name ONLY refers to a portion of the taxon [the native portion] and not the taxon as a whole. The result is that the non-native subspecies CAN be sold. A further consequence is that regulations on the exotic species have to be looked at more closely - Notophthalmus viridescens red-spotted newt is prohibited, but by this precedent, that can ONLY refer to N.v.viridescens, as only that subspecies has that common name. There are several other such examples, although there is at least one where the situation is reversed: The native Ambystoma macrodactylum krausei is only referenced to the species level in both names, rendering all subspecies potentially protected [even though non-native taxa are unprotected]. I'll have to go back and do another reading, because I know there are a couple examples of wording which have the effect of completely changing status for some animals.
I would note that the likely reason the Alberta courts have ruled in this way is because the two names are not in conflict - one is simply a more specific example of the other. In law, that has the effect of acting as an adjective, and the law can ONLY be applied to the full definition. To clarify, if the law says that "tiger salamander" is prohibited, that CANNOT be taken to mean "salamander" is prohibited - only salamanders which are tiger salamanders. The clause must be interpreted in its entirety. It appears to me that the California law falls into this exact situation and would thus be open to a court challenge on that basis. The common name and scientific name are not in conflict, so the scientific name cannot take priority - the law should apply when BOTH names do, and not when only one does.