Joining tables inflates number values - sql

Question

Here is my query, I have different account values (the accValByProd table) that I want to add to my table by their product type. If I just select the accValByProd table by itself the numbers are accurate, but when I join it with the billing table the numbers become much larger than they should be.
As you can see since I need to take the MAX of values in the billing table and then SUM them in the final calculation, I can't just do that in the final SELECT (unless there's a way to do that?). Any help is appreciated I'm not quite sure what I'm doing wrong.
WITH billing AS
( SELECT
bh.debit_account_id,
bh.period_start_date,
bh.period_end_date,
bh.a_id,
bh.account_value,
bh.platform_fee
FROM
billing_history bh
WHERE
-- LESS than same day following year includes any
-- possible time portion if so part of.
bh.period_start_date >= '2020-07-01'
and bh.period_end_date < '2021-07-01'
and bh.a_fee != 0
),
acc_prods AS
(
SELECT
a.account_id,
a.product_id,
CASE WHEN p.product_type = 3 THEN 'FSP'
WHEN p.product_type = 6 THEN 'APM'
WHEN p.product_type = 13 THEN 'UMA'
ELSE 'Unknown' END product_type,
a.a_id
FROM
account a
LEFT JOIN product p
ON a.product_id = p.product_id
WHERE
-- which table alias, should never leave blind
-- assumption here is "Account" table (alias a)
a.close_date IS NULL
OR a.close_date >= GETDATE()
),
accounts AS (
SELECT
a.account_id,
a.a_id,
a.customer_id,
a.close_date
FROM
account a
),
accValByProd as
(
SELECT
bh.debit_account_id AS deb_id,
bh.period_end_date,
MAX(bh.account_value) AS acc_val,
bh.a_id,
ISNULL(ap.product_type, 'Unknown') AS prod_type
FROM
billing_history bh
LEFT JOIN acc_prods ap
ON bh.debit_account_id = ap.account_id
WHERE
bh.period_end_date = '2021-06-30'
GROUP BY
bh.debit_account_id,
bh.period_end_date,
bh.a_id,
ap.product_type
)
SELECT DISTINCT
ad.ad_id,
ad.fname + ' ' + ad.middle + ' ' + ad.lname 'full name',
accValByProd.prod_type AS 'product type',
COUNT(DISTINCT billing.debit_account_id) AS 'number of accounts',
SUM(accValByProd.acc_val) AS 'product aum',
SUM(CASE WHEN DATEDIFF(DAY, billing.period_start_date, billing.period_end_date) > 31
THEN billing.platform_fee ELSE 0 END) AS 'fees'
FROM
advisor ad
JOIN billing
ON ad.a_id = billing.a_id
JOIN accounts
ON billing.debit_account_id = accounts.account_id
JOIN accValByProd
ON billing.debit_account_id = accValByProd.deb_id
WHERE
1=1
and ( ad.termination_date IS NULL
OR ad.termination_date >= GETDATE())
AND ( accounts.close_date IS NULL
OR accounts.close_date >= '2021-06-30')
GROUP BY
ad.a_id,
ad.fname,
ad.middle,
ad.lname,
accValByProd.prod_type
Here are the expected results for a_id 6835 (plus the other information)
a_id product aum product type
---- ------------ -------------
6835 7861895.23 APM
6835 47059722.64 FSP
6835 9816992.32 UMA
6835 528930.47 Unknown
And here are the actual results:
a_id product aum product type
---- ------------ -------------
6835 45447953.20 APM
6835 203942000.07 FSP
6835 77678383.30 UMA
6835 1706276.86 Unknown