The confusion arises because finished operates both as an adjective and as the past tense and past participle of the verb to finish.

So if your colleagues say 'We're finished for today', they are using it as an adjective.

If they say 'We've finished work for today', they are using it as the past participle of the verb to finish. (This would be more normal in standard English).
 

-ed as an adjective

When we use it as an adjective, we can talk about things being finished as well as people being finished with something:

• Their marriage is finished. It was a disaster from the beginning, so it's good it's over.
• She's not ready to leave. She won't be finished for at least another hour and a half.
• Sheila wasn't finished with Paul yet. They still had a lot to talk about.

There are, of course, a wide range of adjectives ending in -ed which follow the verb to be and other linking verbs such as seem, appear, look and become. Here are a few of the most common:

• I became interested in the tennis as soon as I heard that ticket prices would be reduced.
• I was bored with the performance and decided to leave as soon as the interval arrived.
• She seemed surprised - even amazed - to see me. She thought I was in the States.
• They were quite satisfied with the arrangement. Sharing the cost suited them both.
• Ned was frightened of Lucie. He was also worried that they might be late back.

Note that all of these adjectives ending in -ed describe people's feelings, mental states or emotional reactions to something. There are many more. Check those you don't know in a dictionary to see how they are used and which prepositions they can be used with:

amused, appalled, confused, delighted, disappointed, excited, pleased, puzzled, shocked, tired, concerned, convinced, determined, prepared, thrilled

-ing as an adjective

There are also a large number of adjectives ending in -ing which relate to verb forms and are used in the same way as -ed adjectives.

Note that these adjectives usually describe things rather than people directly, although they also describe the effect that something has on your ideas and feelings:

• The meeting was very satisfying for all concerned as everybody got what they wanted.
• The play was quite interesting and commented on many aspects of contemporary life.
• These results, Tom, are disappointing and must be very worrying for your parents.
• I don't want to go to the seaside again this year. It's boring.
• His answers were misleading. In fact, everyone thought he was lying.

Here are some more which can be used in the same way. All of these -ing adjectives listed here have their -ed counterparts:

alarming, amusing, annoying, astonishing, charming, confusing, convincing, depressing, disgusting, embarrassing, encouraging, entertaining, humiliating, inspiring, intriguing, refreshing, rewarding, tempting, terrifying, thrilling

Remember:

• The storm was terrifying. I was terrified by it.
  
  
• His offer - three weeks in the Caribbean with nothing to pay! - is tempting and I am tempted to accept it.