How do you read their instructions?
The person asking you the question isn't just interested in what the instructions are, they're interested in your interpretation of the instructions. They want to know if you have noticed any subtle or hidden meaning, and they may want to know why you think you've been given these instructions. For example:
"Our managers have asked us to be careful with what we say about customers to our friends outside of work. How do you read that?"
"If any of our customers hear what we say about them after work it might hurt the company and we will lose our jobs. Our managers are reminding us to be professional even outside of office hours."
The coworkers in your example may also be asking about the tone of the meeting. Was it formal or informal? Did the meeting worry you, or was it good news? Do you think the meeting hinted towards anything? For example, if they were talking a lot about another company perhaps you suspect that your company will be sold to them soon.
In summary, the verb to read in this context is used when someone is asking about what you think about a situation. It has a slightly worried tone, the person asking you probably has negative opinions about the situation but they're asking for your opinions first.