For all those having problems with this plugin on multisite, I’ll share how I got it working.
The plugin doesn’t seem to create “wp_uji_counter” tables required by the secondary sites (e.g. “wp_2_uji_counter”, “wp_3_uji_counter”, etc). This means timer styles can’t be added (well, it tries – but can’t save them anywhere and writes an error to the WordPress log). The “wp_uji_subscriptions” tables exist, so perhaps it was just an oversight by the author, or due to recent changes in WordPress.
Firstly, make sure there you have the timer styles you need already saved in your primary site – this saves you having to create it on each of the secondary sites.
I exported (via phpMyAdmin) the “wp_uji_counter” table, then did a search and replace (replacing all of the text “wp_uji_counter” with “wp_2_uji_counter”). Import the new table back into your database (using phpMyAdmin again).
Rinse and repeat for all secondary sites.