This is definitely wrong! "A" here should be a tense of the verb "haver" since the meaning is that there is some time that has elapsed. Therefore, it should be "há" and not "a". In European Portuguese, this confusion would be impossible, since the "há" is an open vowel, and "a" by itself is closed.
Another way to see this is the following: in EP, the sound of "à" and "há" is exactly the same, an open "ah". That is the sound we use in this expression. Since we don't always do that ("a" sounds more or less like "uh") the only possible writings are those two. But "à" is always a contraction of a preposition "a" with the article "a" (both alone sound like "uh"). But the article is inflected, and so "a" corresponds only to the case "feminine singular". So it can not make sense with "10 anos", because this is masculine plural. So it would be grammatically wrong. Now, "há" is a verb, and as such "10 anos" is a predicate, and it does not have to agree with the verb itself. It therefore can change in gender and number without changing "há", which is the case. We can say "há uma semana" (fs), "há dois meses" (mp), "havia muito tempo" (masculine singular, but in the past. Since it is a verb, the tense can actually change. But note that "haver" is always impersonal when not used as an auxiliary, so it is can not be the plural "haviam". This is a common mistake nowadays, although in other kind of phrases).
You are right, it is considered redundant in Portuguese. People often use this construction, but according to grammar, they are wrong.
I don't agree with aileigc, that if you leave "há" out and put just "atrás", people would ask "behind what", because this is a widespread expression. They would definitely understand that as meaning "ago".
And, at least to me, this sounds very annoying, and not at all emphasized. People just say this expression because this is a very very often error, and what is repeated many times, seems to be correct.
I think you could say it is redundant. But you could also say it is in there for emphasis :) As leaving "há" out, I don't know. It does sound very fishy to me, it seems to be implying something started 10 minutes behind something else, that is not explained. Like "começou 10 minutos atrás": de quem? do quê?
Vivisaurus tells me that she isn't sure of the rule, but that if you wanted to say "You started..." then you would say "Você começou..." because começou could refer to a number of different pronouns.
Because of that, it's not that "You started..." should be wrong necessarily (she thinks), but that "It started..." is assumed to be the case unless there is obvious context indicating otherwise.
Children: in Portuguese (according to grammar) the correct correspondance to this frase is just: "começou há dez minutos". Here, we're not using the preposition "a" (= "to"), but the verb "há" (="there is") in the sense of elapsed time. And besides, we do not use "há" + "...... atrás", because it is a redundancy. In English it would sound like this: "ten minutes ago ago". The verb "há" is already showing direction of elapsed time. I've reported this to Duolingo.