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I'm a beginner in Japanese. At my classes I'm taught like this: とまる / とめる is a
pair intransitive/transitive verb.

This I understand and can memorize a table of such verbs.

I can't help, though, notice a certain phonetic change pattern in all those
pairs. To this pattern in my classes I was given no explanation.

I wonder if there is any theoretical grammar explanation of that pattern for
those Japanese verbs. Unfortunately, I'm not aware of any good Japanese
theoretical grammar textbook.

(In my native language and in some other languages I know
transitive/intransitive is a lexical, not grammatical category, so I wonder,
if that transitive/intransitivre explanation for Japanese is correct at all)
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question
transitivity
とまる / とめる and such pairs of verbs
Historically, Japanese has had several morphemes that change the transitivity
of a verb. Most of these pairs involved lexicalised combinations of some verb
with one of these morphemes.

The morphemes are:

-(a)su - causative. You can see it in words like ゆらす ('cause to shake', compare ゆれる 'shake').

-(a)ru - passive, or rather, general agent deletion (English's passive implies an agent, this doesn't). Visible in your example とまる ('come to a stop on one's own', compare とめる 'cause something else to stop').

-e(ru) - a kind of transitivity flipper, it can make transitives intransitive or intransitives transitive. An example of the first is さける ('split open', compare さく 'tear'), and an example of the second is つける ('attach', compare つく 'stick to').

Many of these pairs, とめる~とまる included, seem to have had these morphemes added
to both members.

I'm not sure this is a grammatical process, at least any more; none of these
morphemes are still productive as far as I know. You're probably best off
remembering each word as a single lexical unit, especially considering the
fact that there's a good deal of variation among what pairs up with what. Just
remembering that あげる is 'raise' and あがる is 'rise' prevents you from trying to
make non-words like *あがす or *あぐ.

(The Middle Japanese -(a)su and -(a)ru were nidan verbs, and became the
ichidan -(a)seru and -(a)reru, which are still extremely productive in Modern
Japanese. I don't have an explanation for why verb forms that incorporate them
are godan.)
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answer
(My answer partly builds off of Siveru's answer.)

The Dictionary of Basic Japanese Grammar (DBJG) gives an appendix (number 3)
of intransitive/transitive patterns which probably includes all the pairs you
have been given plus a few more. When I first began to study I was able to
learn the pairs in my text book but found the appendix a bit too much. Looking
at that list now I would say that I picked up almost all those pairs
"organically" have not regretted taking that approach because there are other
more important things to memorize.

**However** ( **Updated in response to comments** ):

There were a couple of "verb-families" in the -eru (Intransitive)->
u(Transitive)section which I still found sticky because they seem more like
triplets or "pairs of pairs" and I sometimes had to double check if I had not
used them for a while! These included:

> 破れるー＞破る (splitting/separating things like broken hearts and making holes)  
>  破けるー＞破く (tearing thin things)

An example of a "triplet", not in the appendix is

> つかむ／つかまる／つかまえる

For these I try to remember:

> ロープをつかむ ｜ grab a rope
>
> Aが〜につかまる ｜hang on to a rope
>
> 魚を捕まえる ｜catch a fish
>
> 〜が捕まる ｜be caught

Needless to say I do looking for patterns and today, Silverju's morphemes
resolved this triplet for me:

> a(ru); つかむ->つまる and the flipper e(ru); つかまるー＞つかまえる

The same also applies to my other hated triplet

> つなく／つながる／つなげる.

This is how I currently remember it:

> PCを インタネットにつなぐ (= アクセスする)
>
> 犬を門につないでおく =つなげる

ie:

> 自＝ 〜がつながる （＝＞〜がつながっている）  
>  他＝ 〜をつなぐ＝つなげる

But, applying the morphemes given above:

> -(a)ru:つなぐ ー＞ つながる; and the flipper-e(ru)ー＞つなげる
>
> ie Transitive -> intransitive - > Transitive

(Thanks Silveru.)
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answer