The problem is that your query is non deterministic. You are selecting more columns that you are grouping by where the additional columns are not determined by the columns you are grouping by. If the latter had been true, then this would fall into the ANSII standards of SQL, since it is not it is (in my opinion) a failure of MySQL that it allows the statement to run at all. Other DBMS have gone the opposite way, since they cannot determine if certain columns are functions of other columns not contained in the group by, they will now allow any statement with columns in the select list that are not contained within the group by.
To try and simplify the problem take the following dataset (Table T)
ID Col1 Col2
1 1 1
2 1 3
Running this:
SELECT Col1, MAX(Col2) AS MaxCol2, MIN(Col2) AS MinCol2, AVG(Col2) AS AvgCol2
FROM T
GROUP BY Col1
Will always return
Col1 MaxCol2 MinCol2 AvgCol2
1 3 1 2
However, if you throw ID into the mix
SELECT ID, Col1, MAX(Col2) AS MaxCol2, MIN(Col2) AS MinCol2, AVG(Col2) AS AvgCol2
FROM T
GROUP BY Col1
There is no way of determining which ID will be returned, 1 or 2, the most likely result is
ID Col1 MaxCol2 MinCol2 AvgCol2
1 1 3 1 2
However there is nothing defined in the SQL to state that the result could not be:
ID Col1 MaxCol2 MinCol2 AvgCol2
2 1 3 1 2
So if if the above was the result set, and you added HAVING ID = 1 to the query, you would get no results due to the point at which the HAVING clause is applied to the data. If you were to Add ID to the GROUP BY you would end up with 2 rows, which as I understand it is not what you want, and if you were to add it to the WHERE your MIN, MAX and AVG functions would be affected. So you need to use a subquery. So in this example I would use
SELECT T.ID, T.Col1, MaxCol2, MinCol2, AvgCol2
FROM T
INNER JOIN
( SELECT Col1, MAX(Col2) AS MaxCol2, MIN(Col2) AS MinCol2, AVG(Col2) AS AvgCol2
FROM T
GROUP BY Col1
) T2
ON T.Col1 = T2.Col1
WHERE ID = 1 -- OR ID = 2 DEPENDING ON REQUIREMENTS
To apply this to your situation, the database engine has deteremined that the row that will be returned for the columns not in the group by is the row containing ID = 29. So your HAVING Clause is only being applied to this row, the rows with user1@tyd.fr, and user10@tyd.fr in have already been removed from the results by the time your HAVING clause is applied. You need to perform the aggregate functions separately to the filtering.
Now I haven't fully got my head around your schema, but I am hoping I have explained the issue of the non deterministic statement well enough that you can make any ammendments required to my attempt at rewriting your query
SELECT Avg_Price,
Cnt,
tyd.id_marchand,
tyd.id_product,
catalog.price AS c_price,
tyd.price AS t_price,
tyd.amount AS t_am,
pro_tyd.amount AS p_am,
pro_tyd.price AS p_price,
catalog.img_src,
tyd.step,
tyd.login AS tyd_l
FROM Catalog
INNER JOIN tyd
ON catalog.id_marchand = tyd.id_marchand
AND catalog.id_product = tyd.id_product
INNER JOIN Pro_tyd
ON tyd.id_marchand = pro_tyd.id_marchand
AND tyd.id_product = pro_tyd.id_product
INNER JOIN
( SELECT ID_Marchand, ID_Product, Step, AVG(tyd.price) AS avg_price, COUNT(tyd.id_product) AS cnt
FROM Tyd
WHERE Step = '1'
GROUP BY ID_Marchand, ID_Product, Step
) Agg
ON Agg.id_marchand = pro_tyd.id_marchand
AND Agg.id_product = pro_tyd.id_product
AND Agg.Step = tyd.Step
WHERE tyd.Login = 'user1@tyd.fr'
