A lot of this comes down to how you define voter anonymity, and which failure modes you are trying to protect against.
Regarding the counting of your vote, you have basically the same protections and risks as someone casting a regular ballot. If you don't trust the system organizing the election, then you can't know with certainty your vote will be counted (or not) according to law, regardless of whether it's provisional or not, since it's always possible for a sufficiently corrupt system to create a "wrong", but believable result from thin air. The Help America Vote Act of 2002 (HAVA) requires that
The appropriate State or local election official shall establish a free access system (such as a toll-free telephone number or an Internet website) that any individual who casts a provisional ballot may access to discover whether the vote of that individual was counted, and, if the vote was not counted, the reason that the vote was not counted, though not the result which was recorded for it.
so if you trust the voting system, you can find out whether or not your vote was counted.
Regarding keeping your vote anonymous, state rules vary, but the vote would typically be stored separately, but securely, with a 1-1 mapping to a signed affidavit recording your identity. As such, your vote itself is not anonymous, in that a sufficiently motivated election official with the correct access could identify you and your ballot by transgressing a few layers of security. However, there is protection against "regular" citizens easily identifying your vote, or from you being able to use a provisional ballot to sell your vote with the buyer having reasonable certainty you voted in a particular direction. Worldwide, this kind of system is generally considered a reasonable balance between an audited ballot and voter anonymity. Some even go further down the "audible" route. For example, all UK ballots have printed serial numbers and the serial number of the ballot issued to each voter is recorded.