The diminutive ending -ula is common in classical Latin, and arguably productive.
The examples you found are not exceptional.
The linked question does not discuss all the Latin diminutives.
The suffixes listed in the question are all masculine, but there are corresponding feminine and neuter variants.
So the -ulus there implicitly includes -ula (and -ulum).
Not all words have attested diminutive forms. And while there are patterns to forming diminutives, they are only simple for some types of words.
Many Latin nouns ending in -ula were diminutives themselves; but not all (it doesn't seem to be the case for insula). Words ending in -ula sometimes had diminutives where -ula is replaced with -ella, as in fistella ...
Cassell's Latin Dictionary translates the English word "islet" to Latin as parva insula.
The Dictionary of Medieval Latin from British Sources (DMLBS) contains the word insuleta / insuletta, defined as "islet, small island". ( https://logeion.uchicago.edu/insuleta ) But this is not attested until the 13th century (so the late medieval ...
There are agent nouns for all genders.
For example, saltare gives rise to saltator, saltatrix, and saltatrum.
For more details, see this question.
The stem is revealed by the genitive form.
For my three examples they are saltator- (third conjugation), saltatric- (third), and saltatr- (second).
(The stem of rex is reg-, so it has a g instead of a c.)
If you ...
Are there any existing diminutives of agent (-tor/-trix) nouns?
Yes, though the rarest.
Examples for -trix have been already mentioned by @Joonas and @cnread: nutricula, meretricula...
I'd like to add an example for an adjective derived from a -tor word: punctatoriola, as the diminutive of punctatorius from punctator: the reference is Festi Fragm. e Cod. ...