1 week to 10 days should tell the story In the meantime notift the company that sent the cuttings & the shipper (ups etc) mots carry some insurance & can get replacements.
In the future check shipment before acceptin same.

If I were dividing a sucker from a lilac I would retain as much soil around the roots as possible and I would do it before it leafs out.
From your post it sounds like neither was done. Surely this was not purchased from a knowledgeable nurseryman. I imagine that they were cheap but still, get your money back ASAP.
In the future, handle bareroot lilacs only when dormant or else get them established in a pot.
Sam