The word additional is ambiguous because it could modify just local or also long distance.
To start with, it does say All airtime is billed by the second after the first minute. This initially seems to very clearly favor the understanding that additional minutes of any kind, local or long distance, are billed by the second after the first minute. It is an unrestricted and absolute sentence, with no qualifications to it, that clearly addresses all airtime of any kind.
(Now, whether or not the first minute is billed at all is unclear; the first sentence could be stating that the first minute is charged for even if the call lasts less than one minute, or it could be saying that the first minute has no charge at all.)
The interpretation of additional as meaning "outside of some allotted number of free minutes" really has no basis if claimed on the merit of these two sentences alone. The given wording militates against there being any free minutes of any kind at all. The statements do not clearly indicate "in addition to what" the said additional minutes refer to (additional to the first minute, or additional to the free/allotted minutes?). But that is in your favor! Given this glaring omission of how there can be additional minutes of any kind (when it just categorically said ALL airtime after the first minute is billed), it does become quite natural--if the context of all the surrounding language clearly denotes the existence of free minutes--to assume that "additional" refers to minutes "in addition to the free ones."
In the absence of a clear statement elsewhere that free minutes only apply to local calls, I think a good case can be made that a reasonable human being could both misunderstand the intent, and also not recognize that there was any ambiguity. If, however, other language indicates the free minutes can only apply to local calls, then this unfortunate ambiguity can't stand--it has to be interpreted in light of the other information.
In any case, it is very awkwardly and ambiguously worded. Saying "... minutes are $0.10 per minute" is silly! Either "airtime is $0.10 per minute." or "minutes are $0.10 each". Clearly, not all airtime is billed by the second after the first minute. So it shouldn't say that. It has problems.