What is the mechanism for this intramolecular SN1 reaction?
You are correct on your initial assumption. This hydrolysis is assisted by the neighboring thiomethoxy group ($\ce{SCH3}$) as depicted in the following scheme:

The cyclic methylsulfonium intermediate, which is achiral in this case, is a mimic of bromonium ion in bromination of alkenes (also see Chemistry of Sulfur Mustard on releasing chlorine through cyclic alkylsulfonium ion). Realistically, this intermediate is mimic of bromonium ion of of cis-2-butene (also achiral), and hence would give a racemic mixture. Similar to bromonium ion intermediate, the upcoming nucleophile ($\ce{H2O}$) can attack at two places: through path $a$ or through path $b$. Keep track on the (R,S)-configurations of two stereo centers. The original compound has (S,S)-configuration. The (S)-configuration on carbon attached to $\ce{SCH3}$ is unchanged but carbon attached to $\ce{OTs}$ has been changed to (S)-configuration in cyclic intermediate, because it is necessary to have an anti-periplanar conformation for attacking group ($\ce{SCH3}$) and leaving group ($\ce{OTs}$), similar to $\mathrm{E2}$ mechanism.
During the path $a$ mechanism, $\ce{H2O}$ attack the carbon where $\ce{OTs}$ originally was. Therefore, the carbon bearing $\ce{SCH3}$ group does not change its (S)-configuration. However, the $\ce{H2O}$ attack happens in the opposite face of $\ce{SCH3}$ group, the (S)-configuration retain in the carbon bearing $\ce{OH}$ (as in the original compound).
However, both stereochemistry would be reversed during the path $b$ mechanism (see the scheme). Accordingly, $\ce{H2O}$ attack the carbon where $\ce{SCH3}$ originally was, which has (S)-configuration. Since the $\ce{H2O}$ attack happens in the opposite face of $\ce{SCH3}$ group, the (S)-configuration would be changed to the (R)-configuration in this carbon, now bearing $\ce{OH}$. (as in the original compound). The second carbon, now bearing $\ce{SCH3}$ group, would not change its (R)-configuration (as in the cyclic intermediate).
As a result, you get racemic mixture.