Carburetor Vent Lines NOT into Filter

I have the same K&N filters on my Eurostar and the veent pipes are routed externally as shown in your second picture. I don't know whether you should change your installation to match. I'm sure that others will be able to enlighten you.

The standard configuration is to have them just tucked under the bail, as in your second picture; you just want them to have exposure to ambient air pressure.  I would take them out of the filters; I can't think of any good reason for them to be routed there. 

You may be able to patch the hole in your filter to avoid buying new ones, although I do not think new ones are very expensive.

It depends on your airplane configuration.  The vent lines must be at the exact same external air pressure as the float bowl pressure, otherwise the carbs will be too lean or too rich. Most carbs with K&N filters are set up with the vent line under the bail wire of the float bowl. Best recommendation is discuss this with a Rotax mechanic.  Also check out eaa.org/Videos, Dean Vogel (from Lockwood) "Rotax 912 Fuels and Carburetion". His videos explain in detail the mysteries of the Bing carb and Rotax engines:)

I would say the pressure at the vent lines is what determines the float bowl pressure...  and you want that to be ambient, not higher or lower.

The vent lines exist to equalize the pressure between the carb bowl and the Carb external throat.
This allows for the venturi effect in the carb throat to draw the proper amount of fuel from the bowl.
The Carb is calibrated assuming a zero pressure loss across the air filter.
As the filter ages, the pressure drop across the filter medium causes more fuel to be drawn from the float bowl causing an increasingly richer mixture over time.
If the vent tube is attached to communicate directly wih the pressure internal to the Air filter, as the filter ages, the Bowl pressure changes equally to compensate for the change and the mixture remains stable over time.

The engines with Airboxes installed between the Air Filter and the carbs, have their vent tube connected to the air boxes and not to the ambient air.
This arrrangement is especially important if the engines have turbochargers installed.

There is absolutely Nothing wrong with connecting the vent tube to the air filters.
This is actually the preferred configuration.

What is unusual is that the Bing Carbs were designed with external vent tubes and the bowls were not vented to the carb external throat via a simple drilled hole in the carb body connecting the bowl to the throat like most other carbs have.