(Well, first I think you mean moved, not sifted or even shifted.)
I would certainly say: We heard that the Richars had moved house recently (verbs in the past and past perfect)
Or else: We hear that the Richars have moved house recently (verbs in the present and present perfect)
1. We shifted to Chennai in the year 2009.
2. We moved to Chennai last month.
3. We moved house to Chennai last month.
@Shri8 -- I don't think that recently proves it's the present tense, though it does suggest it. It's perfectly possible to say, for instance: "Twenty years ago I moved to Delhi. I had recently been appointed to the post of...", where recently means shortly before.