Are we expected to fly distanced leg (instead of timed leg) in holding pattern in GPS approaches?
Short Answer:
Yes, the pilot is expected to fly the hold as depicted, with an outbound leg based on distance (see AIM 5-3-7, paragraph b). Most holds depicted on GPS instrument approaches in the US now have a specified distance for the outbound hold leg, instead of a timed leg.
Longer Answer:
The traditional hold leg distance is determined by timing. See AIM 5-3-7 § j. 4.:

4. Timing.
(a) Inbound Leg.
(1) At or below 14,000 feet MSL: 1 minute.
(2) Above 14,000 feet MSL: 11/2 minutes.
NOTE- The initial outbound leg should be flown for 1 minute or 1 1/2 minutes (appropriate to altitude). Timing for subsequent outbound legs
should be adjusted, as necessary, to achieve proper inbound leg time.
Pilots may use any navigational means available; i.e., DME, RNAV,
etc., to ensure the appropriate inbound leg times.
(b) Outbound leg timing begins over/abeam the fix, whichever occurs
later. If the abeam position cannot be determined, start timing when
turn to outbound is completed.

In years past this was common for all holds, unless otherwise specified by the published hold instructions, or by ATC. All otherwise unspecified holds were assumed to be timed holds, including for GPS approaches. I only remember a few distance-defined holds in my local area from 10 years ago; now all those holds associated with GPS instrument approaches are distance defined.
Which brings us to the AIM 5-3-7 § j. 5. (emphasis on the last two sentences is mine):

5. Distance Measuring Equipment (DME)/ GPS Along-Track Distance (ATD). DME/GPS holding is subject to the same entry and holding procedures except that distances (nautical miles) are used in lieu of time values. The outbound course of the DME/GPS holding pattern is called the outbound leg of the pattern. The controller or the instrument approach procedure chart will specify the length of the outbound leg. The end of the outbound leg is determined by the DME or ATD readout. The holding fix on conventional procedures, or controller defined holding based on a conventional navigation aid with DME, is a specified course or radial and distances are from the DME station for both the inbound and outbound ends of the holding pattern. When flying published GPS overlay or stand alone procedures with distance specified, the holding fix will be a waypoint in the database and the end of the outbound leg will be determined by the ATD. Some GPS overlay and early stand alone procedures may have timing specified.

See also AIM Fig 5-3-7 and the associated note, which address the type of distance holds found on GPS approaches:


NOTE-
The inbound course is always toward the waypoint and the ATD is zero at the waypoint. The end of the outbound leg of the holding pattern is reached when the ATD reads the specified distance.

The holds found on GPS approaches will generally be distance based. The AIM states that some might still be time based, but I am no longer aware of any such holds in actuality. Every approach that I know of that used to have a time based hold on a GPS approach now has a distance based hold.
All holds should be flown as published or as instructed by ATC. If ATC does not instruct you otherwise, you are expected to fly the hold as published. In this case, that means you are expected to fly the hold as a distance-based hold. If you are not sure how you should fly the hold, ask ATC. They will provide you with the complete holding instructions if requested. See AIM 5-3-7 § b.:

b. If the holding pattern is charted and the controller doesn't issue
complete holding instructions, the pilot is expected to hold as
depicted on the appropriate chart. When the pattern is charted, the
controller may omit all holding instructions except the charted
holding direction and the statement AS PUBLISHED; e.g., HOLD EAST AS
PUBLISHED. Controllers shall always issue complete holding
instructions when pilots request them.