I just felt like I wanted to make a brief rundown of the story with hard and soft consonants.

The first thing to start off is that the English language does not have soft consonants. Which means that even when an anglophone says an "ee" sound (as in leap), they don't soften the first L. So the vowel does not affect the consonant that is running ahead of it. However, In Russian, it does. The so called soft vowels (яеиёю) and the soft sign turn the preceding consonant to its palatalized analog. So they kind of, run together, in pairs -- soft consonant + soft vowel and hard consonant + hard vowel.

When a word starts in a soft vowel without a consonant running in front of it, we have to lift the tongue in the palatalized position in order to get the vowel sound right. It's very similar to pronouncing an Й sound, or a Y as in You (technically it's a j according to the IPA), but most of the people project this principle onto the cases where there is a consonant in front of the vowel, and just sneak in this j sound inbetween the consonant and the vowel, without softening the consonant, which is a mistake.

In this case, the whole thing sounds like MjASO (мясо - meat), which is not right. The M should not stay hard. It should go palatalized and turn into a M', and then you just don't need this j subsound as your tongue is already in the correct position to go with the vowel.
This kind of thing sticks out like a sore thumb and is being easily recognized by native speakers of Russian, revealing the fact that they are talking to a foreigner, and sometimes causing confusion and misunderstanding.