I wish I had a good answer for you. Pop Trivialis is difficult to get rid of. 

How extensive it is will probably determine your course of action. You can try to pull it if it is not too extensive. It is intolerant of dry soil so it may be easier to get at this summer if we reach a dry spell. 

Do not over irrigate your lawn. 

If you choose to use an herbicide you will have to reseed the areas because it will kill all the grass in the treated area. 

Are you certain of your identification? One of your photos shows seed heads which is more likely to be poa annua. If this is the case you can use a pre-emergent next year. 

https://plants.ces.ncsu.edu/plants/poa-annua/

https://apps.extension.umn.edu/garden/diagnose/weed/grass/roughbluegrass.html

https://extension.psu.edu/lawn-and-turfgrass-weeds-roughstalk-bluegrass-poa-trivialis-l

https://turf.purdue.edu/poa-annua-poa-trivialis-in-lawns-and-athletic-fields/

It does not say anywhere on the label that this herbicide is effective on Poa Trivialis.  It does say that it is not effective on sedges. 

We don;t recommend using any herbicide unless the label specifically states that it will be effective on the plant you want to get rid of. 

This is highly toxic to fish and aquatic systems so if you are near a water system I wouldn’t’t use it either. 

If you do try it, be sure to follow all label instructions, buy only what you need now, and wear protective clothing.

https://transportation.ky.gov/Maintenance/Pesticides/Acclaim%20Extra.pdf

It’t impossible to tell if it was in the sod or the soil. 

Sorry.

I can’t give you a good answer to that question. What was there before you hired the landscaper to lay sod? Did they scrape the area clean before laying the sod? Did they use any weed killer prior to laying the sod? 

You will have to have this conversation with your contractor.