It could be dangerous to rely too much ultimately on one piece of hearsay:
' I have heard the Big firms only ask time of employment/position/ etc and nothing about performance '
Its not necessarily always going to be wrong but it might not always be right either. I can think of several exceptions to this and cliche reasons that it varies by level.
Its not explicit whether your 4 month role is going to be referenced as average or poor. Ask (yourself or better still them) how sub-excellent it was (perhaps phrase it more carefully!). Employers may not actually request it.
If it is average and they also consider your other experiences, then you should indeed be fine.