BUG: Groupby rolling count gives inconsistent outputs with missing index 
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

#### Code Sample, a copy-pastable example

```python
# [1] In:
import pandas as pd

assert pd.__version__ == "1.3.2"

df = pd.DataFrame(
    {
        "id": ["a", "a", "b", "b", "b"],
        "timestamp": pd.date_range("2021-9-1", periods=5, freq="H"),
        "y": range(5),
    }
)
df
```

```python
# [1] Out:
  id           timestamp  y
0  a 2021-09-01 00:00:00  0
1  a 2021-09-01 01:00:00  1
2  b 2021-09-01 02:00:00  2
3  b 2021-09-01 03:00:00  3
4  b 2021-09-01 04:00:00  4
```

```python
# [2] In: 
grp = df.groupby("id").rolling("1H", on="timestamp")
grp.count()  
```

```python
# [2] Out: 
# original index [0,1,2,3,4] is in output
               timestamp    y
id                           
a  0 2021-09-01 00:00:00  1.0
   1 2021-09-01 01:00:00  1.0
b  2 2021-09-01 02:00:00  1.0
   3 2021-09-01 03:00:00  1.0
   4 2021-09-01 04:00:00  1.0
```

```python
# [3] In:
grp["y"].count()  
```

```python
# [3] Out:
# original index [0,1,2,3,4] is missing in output as opposed to [2] Out
id  timestamp          
a   2021-09-01 00:00:00    1.0
    2021-09-01 01:00:00    1.0
b   2021-09-01 02:00:00    1.0
    2021-09-01 03:00:00    1.0
    2021-09-01 04:00:00    1.0
Name: y, dtype: float64
```

```python 
# [4] In:
grp.count()  # same as [2] In
```

```python
# [4] Out:
# output is inconsistent with that from [2] Out
                       timestamp    y
id timestamp                         
a  2021-09-01 00:00:00       NaT  1.0
   2021-09-01 01:00:00       NaT  1.0
b  2021-09-01 02:00:00       NaT  1.0
   2021-09-01 03:00:00       NaT  1.0
   2021-09-01 04:00:00       NaT  1.0
```
#### Expected Output
1. `[4] Out` should be identical to `[2] Out` 
2. I as a user would hope original index is, at least optionally if not by default, kept in output so I can efficiently join the rolling count results back to the original `df`. 

#### Problem description
1. Groupby rolling count gives inconsistent outputs (see `[2] Out` and `[4] Out`) when running cell 1~4. Same problem exists when `count` is replaced by `agg(len)` 
2. `[3] Out` using pandas 1.3.2 ignored original index whereas `[2] Out` (as well as `[3] Out` using pandas 1.1.5 ) maintained original index. Original index (in this example, `[0,1,2,3,4]`) should ideally be optionally kept in outputs otherwise there will be no way to traceback which rolling count corresponds to the original row (see `[3] Out`). Joining two data frames on `['id', 'timestamp']` afterwards is not the correct solution as it is easy to find non 1-1 match examples. 

```python
# [3] Out: pandas 1.3.2
# original index [0,1,2,3,4] is missing. 
id  timestamp          
a   2021-09-01 00:00:00    1.0
    2021-09-01 01:00:00    1.0
b   2021-09-01 02:00:00    1.0
    2021-09-01 03:00:00    1.0
    2021-09-01 04:00:00    1.0
Name: y, dtype: float64
```

```python 
# [3] Out: pandas 1.1.5
# original index [0,1,2,3,4] maintained as expected though the rolling count numbers are wrong (should be [1,1,1,1,1])
id   
a   0    1.0
    1    2.0
b   2    1.0
    3    2.0
    4    3.0
```


#### Output of ``pd.show_versions()``

<details>
INSTALLED VERSIONS
------------------
commit           : 5f648bf1706dd75a9ca0d29f26eadfbb595fe52b
python           : 3.8.10.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.14.225-121.362.amzn1.x86_64
Version          : #1 SMP Tue Mar 23 00:29:14 UTC 2021
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.2
numpy            : 1.20.3
pytz             : 2021.1
dateutil         : 2.8.2
pip              : 21.2.4
setuptools       : 57.4.0
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : 4.1.2
blosc            : None
feather          : None
xlsxwriter       : 3.0.1
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 3.0.1
IPython          : 7.26.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : 2021.07.0
fastparquet      : None
gcsfs            : None
matplotlib       : 3.4.3
numexpr          : None
odfpy            : None
openpyxl         : 3.0.7
pandas_gbq       : None
pyarrow          : 5.0.0
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.6.3
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
