one of the meanings of "be+...+oftadan" is used to explain who and why some reasons caused I do something or I place in that situation.

when you are talking about a seri of aspects and sutuations and ... that made you do something is the basic case inwhich we use be+(noun) or (verb) +oftadan(conjugated of this infinitive)

oo be gerye oftad, note: before this sentence narator was talking about this history and when he/or she says :"oo be gerye oftad" you know why. for example:

dashtand axhaye ghadimi ra mididand, nagahan oo be geryeh oftad.

they were reviewing their old pics, suddenly she started to cry. yeah in this case we should translate it in this way but mostly we wanted to highlight that an unexpected action happened when we can guess why.

this structure is just for certain verbs and nouns so you can not expand this rule for every words in persian.

but you are right sometimes it means :start to+..., cheshmam be khaaresh oftadand.

it means my eye(s) started to itch, then one should ask "why?what happened?" if the reason wasn't clear.

what's the difference between "be+...+oftadan" and "be +...+ andakhtan"?

the first one is the passive form of second one. so mentioned website is right.

oo man ra be geryeh andakht, she made me crying.

for my money it's the passive form of make someone+... rather than starting .... in most of the sentences. so forget about what you read in these pdfs while they just wanted to write an example and they didn't teach the usage of this verb considering its expressed meaning in detail.

good luck