Gas Furnace/Water Heater Vent Issue?

I have a two gas appliances - furnace (forced air) and water heater (no fan) -that vent into my chimney (see pics). I recently had a repair performed on my furnace and the technician said my venting was installed incorrectly. Specifically, she said the wye connection should have been installed on the outside part of the chimney NOT within the chimney itself (see pics). I can’t remember her exact words but she said it would be difficult to check the condition on the liner in this particular instance and recommended we have this corrected.

What do you make of this pictures? Do I have a real problem here?

Looks like your flue vent off the furnace starts out off the manifold discharge with single wall, then converts to double wall elbow (B-vent) prior to connecting over the single wall wye into the chimney. Also looks like the vent piping off the water heater is all single wall, tieing into the wye. If all that is correct, you need to correct. If incorrect, you still should get at least another opinion. Have you verified that your chimney has a proper terra-cotta or other type certified liner, and in good condition.

Yes wrong.
The connection is buried in cement.

looks like the furnace flue pipe is reduced before it ties into the y connection.